K-theory of certain purely infinite crossed products

TL;DR

This paper explores how different construction choices in group actions on compact spaces can lead to varied Kirchberg algebras, focusing on free groups and their K-theoretic properties.

Contribution

It demonstrates that for free groups, different construction choices can produce distinct purely infinite crossed product C*-algebras.

Findings

Different choices in the construction lead to non-isomorphic algebras.

The work extends understanding of the K-theory of purely infinite crossed products.

It highlights the impact of construction choices on algebraic properties.

Abstract

It was shown by Rordam and the second named author that a countable group G admits an action on a compact space such that the crossed product is a Kirchberg algebra if, and only if, G is exact and non-amenable. This construction allows a certain amount of choice. We show that different choices can lead to different algebras, at least with the free group.