Selfless nonnuclear crossed products

Abstract

For a strictly ergodic action of a countable discrete group with Ozawa's property PHP on the Cantor set, we prove that dynamical comparison implies complete selflessness of its reduced crossed product. Therefore these crossed products have stable rank one, strict comparison, a unique quasitracial state, and real rank zero. Applications include probability-measure-preserving Cantor actions of C*-simple acylindrically hyperbolic and C*-simple linear groups for which an infinite amenable subgroup acts strictly ergodically. The results also apply to subodometers and infinite regular Toeplitz subshifts of residually finite groups with PHP.

arXiv commentv3. New examples added, references updated, and typos fixed; 24 pages, 2 figures