Selfless Reduced Crossed Product $C^{*}$-Algebras Arising from Almost Periodic Actions

Abstract

We prove that the reduced crossed product $C^*$-algebras of almost periodic actions of countable discrete groups having a topologically free extreme boundary on unital, separable, simple, exact, $\mathcal{Z}$-stable and monotracial $C^*$-algebras are selfless.We combine Ozawa's "tree-graded'' space method with the theory of strong convergence of indexed families for the proof.