Ergodic automorphisms on Kirchberg algebras

Abstract

Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Kirchberg algebra. In the proof, we give a Pimsner construction realizing many unital subalgebras of a given unital Kirchberg algebra as the fixed point algebras of single automorphisms. Furthermore, for amenable infinite discrete groups, we show that every point-wise outer action on arbitrary unital Kirchberg algebra has an ergodic cocycle perturbation with the help of Gabe--Szab\'{o}'s theorem and Baum--Connes' conjecture.