Strict comparison for twisted group C*-algebras

Abstract

We prove that any reduced twisted group C*-algebra of a selfless group with the rapid decay property is selfless. As an application, we show that twisted group C*-algebras of acylindrically hyperbolic groups (possibly with nontrivial finite radical) and rapid decay are pure, and hence have strict comparison.

7 pages; v3 included references to more recent results, minor modifications; v2 generalized from finitely generated to countable groups