Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra

Abstract

Let A and B be simple separable nuclear monotracial C⁎-algebras, and let α and β be strongly outer actions of a countable discrete amenable group Γ on A and B, respectively. In this paper, we show that α⊗idW on A⊗W and β⊗idW on B⊗W are cocycle conjugate where W is the Razak-Jacelon algebra. Also, we characterize such actions by using the fixed point subalgebras of Kirchberg's central sequence C⁎-algebras.