#### Volume 13, issue 2 (2013)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Other MSP Journals
The Künneth Theorem in equivariant $K$–theory for actions of a cyclic group of order $2$

### Jonathan Rosenberg

Algebraic & Geometric Topology 13 (2013) 1225–1241
##### Abstract

The Künneth Theorem for equivariant (complex) $K$–theory ${K}_{G}^{\ast }$, in the form developed by Hodgkin and others, fails dramatically when $G$ is a finite group, and even when $G$ is cyclic of order $2$. We remedy this situation in this very simplest case $G=ℤ∕2$ by using the power of $RO\left(G\right)$–graded equivariant $K$–theory.

##### Keywords
Künneth theorem, equivariant $K$–theory, $\operatorname{RO}(G)$–graded
##### Mathematical Subject Classification 2010
Primary: 19L47
Secondary: 19K99, 55U25, 55N91