On the classification of group actions on C*-algebras up to equivariant KK-equivalence

Abstract

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of Izumi is equivalent to an equivalence between cocycle conjugacy and equivariant KK-equivalence for actions of torsion-free amenable groups on Kirchberg algebras. Let G be a cyclic group of prime order. We describe its actions up to equivariant KK-equivalence, based on previous work by Manuel Köhler. In particular, we classify actions of G on stabilised Cuntz algebras in the equivariant bootstrap class up to equivariant KK-equivalence.

added two references and replaced conjugacy by cocycle conjugacy in introduction made a number of changes, leading to different theorem numbering in some sections

References in corpus (2)

• Equivariant Kirchberg-Phillips-type absorption for amenable group actions
• A more general method to classify up to equivariant KK-equivalence II: Computing obstruction classes

Cited by in corpus (2)

• The spectrum of equivariant Kasparov theory for cyclic groups of prime order
• Bundles of strongly self-absorbing $C^{\ast }$-algebras with a Clifford grading