<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262022000100035</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v56n1.105613</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Induced character in equivariant K-theory, wreath products and pullback of groups]]></article-title>
<article-title xml:lang="es"><![CDATA[Carácter inducido en K-teoría equivariante, productos wreath y pullbacks de grupos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Combariza]]></surname>
<given-names><![CDATA[German]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodriguez]]></surname>
<given-names><![CDATA[Juan]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Velasquez]]></surname>
<given-names><![CDATA[Mario]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Fundación Universitaria Konrad Lorenz  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,École normale supérieure de Lyon  ]]></institution>
<addr-line><![CDATA[Lyon ]]></addr-line>
<country>France</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>56</volume>
<numero>1</numero>
<fpage>35</fpage>
<lpage>61</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262022000100035&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262022000100035&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262022000100035&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Let G be a finite group and let X be a compact G-space. In this note we study the (Z + ( Z /2Z)-graded algebra    defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of F q G (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of F q G(H (X ( Y) in terms of F q G (X) and F q H (Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Sea G un grupo finito y X un G-espacio compacto. En esta nota estudiamos el álgebra (Z + ( Z /2Z)-graduada    Definida en términos de K-teoría equivariante con respecto a productos guirnalda, como un álgebra simétrica, revisamos algunas de las propiedades de F q G (X) probadas por Segal y Wang. Probamos una formula tipo Kunneth para estas álgebras graduadas, más específicamente, sea H otro grupo finito y Y un H-espacio compacto, nosotros damos una descomposición de F q G(H (X(Y) en términos de F q G (X) y F q H (Y), para esto, debemos estudiar la teoría de representaciones de pullbacks de grupos. Discutimos también algunas aplicaciones de los resultados anteriores a K-homología equivariante conectiva.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[equivariant K-theory]]></kwd>
<kwd lng="en"><![CDATA[wreath products]]></kwd>
<kwd lng="en"><![CDATA[Fock space]]></kwd>
<kwd lng="es"><![CDATA[K-teoría equivariante]]></kwd>
<kwd lng="es"><![CDATA[productos wreath]]></kwd>
<kwd lng="es"><![CDATA[espacio de Fock]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Atiyah]]></surname>
<given-names><![CDATA[M. F.]]></given-names>
</name>
</person-group>
<source><![CDATA[K-theory, second ed., Advanced Book Classics]]></source>
<year>1989</year>
<publisher-loc><![CDATA[Redwood City, CA ]]></publisher-loc>
<publisher-name><![CDATA[Addison-Wesley Publishing Company Advanced Book Program]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Atiyah]]></surname>
<given-names><![CDATA[M. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Segal]]></surname>
<given-names><![CDATA[Graeme]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On equivariant Euler characteristics]]></article-title>
<source><![CDATA[J. Geom. Phys]]></source>
<year>1989</year>
<volume>6</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>671-7</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baum]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Higson]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Schick]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the equivalence of geometric and analytic K-homology]]></article-title>
<source><![CDATA[Pure Appl. Math. Q]]></source>
<year>2007</year>
<volume>3</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-24</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Combariza]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Pullbacks with kernel s3]]></source>
<year>2019</year>
</nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dieck]]></surname>
<given-names><![CDATA[T. T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Transformation groups, de Gruyter Studies in Mathematics]]></source>
<year>1987</year>
<volume>8</volume>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Walter de Gruyter &amp; Co]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="">
<collab>The GAP Group, GAP - Groups</collab>
<source><![CDATA[Algorithms, and Programming]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hopkins]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
<name>
<surname><![CDATA[J.Kuhn]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Ravenel]]></surname>
<given-names><![CDATA[D. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized group characters and complex oriented cohomology theories]]></article-title>
<source><![CDATA[J. Amer. Math. Soc]]></source>
<year>2000</year>
<volume>13</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>553-94</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kuhn]]></surname>
<given-names><![CDATA[N. J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Character rings in algebraic topology, Advances in homotopy theory (Cortona, 1988), London Math. Soc. Lecture Note Ser]]></source>
<year>1989</year>
<volume>139</volume>
<page-range>111-26</page-range><publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge Univ. Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lück]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Chern characters for proper equivariant homology theories and applications to K- and L-theory]]></article-title>
<source><![CDATA[J. Reine Angew. Math]]></source>
<year>2002</year>
<volume>543</volume>
<page-range>193-234</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macdonald]]></surname>
<given-names><![CDATA[I. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Zelevinsky]]></surname>
<given-names><![CDATA[A. V.]]></given-names>
</name>
<name>
<surname><![CDATA[Stanley]]></surname>
<given-names><![CDATA[Richard]]></given-names>
</name>
</person-group>
<source><![CDATA[Symmetric functions and Hall polynomials, second ed., Oxford Classic Texts in the Physical Sciences, The Clarendon Press]]></source>
<year>2015</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Milnor]]></surname>
<given-names><![CDATA[J. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Moore]]></surname>
<given-names><![CDATA[J. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the structure of Hopf algebras]]></article-title>
<source><![CDATA[Ann. Of Math]]></source>
<year>1965</year>
<numero>2</numero>
<issue>2</issue>
<page-range>81</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Minami]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Künneth formula for equivariant K-theory]]></article-title>
<source><![CDATA[Osaka J. Math]]></source>
<year>1969</year>
<volume>6</volume>
<page-range>143-6</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Segal]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Equivariant K-theory]]></article-title>
<source><![CDATA[Inst. Hautes Études Sci. Publ. Math]]></source>
<year>1968</year>
<numero>34</numero>
<issue>34</issue>
<page-range>129-51</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Segal]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Equivariant K-theory and symmetric products]]></source>
<year>1996</year>
</nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Serre]]></surname>
<given-names><![CDATA[J.-P.]]></given-names>
</name>
<name>
<surname><![CDATA[Leonard]]></surname>
<given-names><![CDATA[L. Scott]]></given-names>
</name>
</person-group>
<source><![CDATA[Linear representations of finite groups, Springer-Verlag, New York-Heidelberg]]></source>
<year>1977</year>
</nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Velásquez]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A configuration space for equivariant connective Khomology]]></article-title>
<source><![CDATA[J. Noncommut. Geom]]></source>
<year>2015</year>
<volume>9</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1343-82</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Velásquez]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A description of the assembly map for the Baum-connes conjecture with coefficients]]></article-title>
<source><![CDATA[New York Journal of Mathematics]]></source>
<year>2019</year>
<volume>29</volume>
<page-range>668-86</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Equivariant K-theory, wreath products, and Heisenberg algebra]]></article-title>
<source><![CDATA[Duke Math. J]]></source>
<year>2000</year>
<volume>103</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-23</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
