Actions of amenable groups and crossed products of $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebras

Abstract

We study actions of countable discrete amenable groups on unital separable simple nuclear $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebras. Under a certain assumption on tracial states, which is automatically satisfied in the case of a unique tracial state, the crossed product is shown to absorb the Jiang-Su algebra $\mathcal{Z}$ tensorially.