Classification of equivariantly O2-stable amenable actions on nuclear C⁎-algebras

Abstract

Given a second-countable, locally compact group G, we consider amenable G-actions on separable, stable, nuclear $C^{⁎}$-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz algebra $O_2$. We show that such actions are classified up to cocycle conjugacy by the induced G-action on the primitive ideal space. In the special case when G is exact, we prove a unital version of our classification theorem. For compact groups, we obtain a classification up to conjugacy.