On invertible elements in reduced $C^{\ast }$-algebras of acylindrically hyperbolic groups

Abstract

Let $G$ be an acylindrically hyperbolic group. We prove that if $G$ has no non-trivial finite normal subgroups, then the set of invertible elements is dense in the reduced $C^{\ast }$-algebra of $G$. The same result is obtained for finite direct products of acylindrically hyperbolic groups.