Crossed products of inner quasidiagonal C*-algebras

Abstract

In this paper, we show that if $\mathcal{A}$ is an infinite dimensional separable unital inner quasidiagonal $C^*$-algebra, and  $\alpha: G\rightarrow {\rm Aut}(\mathcal{A})$ is an action of a finite group $G$ on $\mathcal{A}$ which has the weak tracial Rokhlin property, and  $\mathcal{A}$ is $\alpha$-simple,  then the crossed product  $C^*(G,\mathcal{A},\alpha)$ is a separable inner quasidiagonal $C^*$-algebra again.