Aperiodic automorphisms of nuclear purely infinite simple $C^{\ast}$-algebras

Abstract

We show that if two aperiodic automorphisms of a separable nuclear unital purely infinite simple $C^{\ast}$-algebra are asymptotically unitarily equivalent, then they are outer conjugate with respect to an automorphism which is isotopic to the identity automorphism. Thus, by Kirchberg and Phillips, they have the same KK-class if and only if they are outer conjugate with respect to an automorphism which is in the KK-class of the identity automorphism.