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.

15 pages, small corrections, to appear in Compositio Mathematica

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