A universal coefficient theorem for actions of finite groups on C*-algebras

TL;DR

This paper establishes a universal coefficient theorem for finite group actions on C*-algebras, enabling classification of certain actions on Kirchberg algebras up to cocycle conjugacy.

Contribution

It introduces a universal coefficient theorem for the localisation of the equivariant bootstrap class at the group order, advancing classification methods for G-actions.

Findings

Bootstrap class generated by functions on G/H for cyclic subgroups H

Universal Coefficient Theorem for the localisation at |G|

Classification of G-actions on Kirchberg algebras

Abstract

The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is already generated by the continuous functions on G/H for all cyclic subgroups H of G. Then we prove a Universal Coefficient Theorem for the localisation of this bootstrap class at the group order |G|. This allows us to classify certain G-actions on stable Kirchberg algebras up to cocycle conjugacy.