Abstract

COMBARIZA, German; RODRIGUEZ, Juan  and  VELASQUEZ, Mario. Induced character in equivariant K-theory, wreath products and pullback of groups. Rev.colomb.mat. [online]. 2022, vol.56, n.1, pp.35-61.  Epub Jan 03, 2023. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n1.105613.

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.

Keywords : equivariant K-theory; wreath products; Fock space.

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