A Fixed Point Decomposition of Twisted Equivariant K-Theory

TL;DR

This paper introduces a new decomposition method for rational twisted G-equivariant K-theory, extending previous decompositions to include twists from group cocycles, and applies it to fixed point spaces.

Contribution

It generalizes existing decompositions of equivariant K-theory to include twisted cases from group cocycles, providing a broader framework for analysis.

Findings

Decomposition of rational twisted G-equivariant K-theory into fixed point space groups

Extension of Atiyah-Segal's untwisted decomposition to twisted cases

Inclusion of group cocycle twists in the decomposition

Abstract

We present a decomposition of rational twisted $G$-equivariant K-theory, $G$ a finite group, into cyclic group equivariant K-theory groups of fixed point spaces. This generalises the untwisted decomposition by Atiyah and Segal as well as the decomposition by Adem and Ruan for twists coming from group cocycles.