Equivariant $\mathcal{O}_2$-absorption theorem for exact groups

Abstract

We show that, up to strong cocycle conjugacy, every countable exact group admits a unique equivariantly $\mathcal{O}_2$-absorbing, pointwise outer action on the Cuntz algebra $\mathcal{O}_2$ with the quasi-central approximation property (QAP). In particular, we establish the equivariant analogue of the Kirchberg $\mathcal{O}_2$-absorption theorem for these groups.