Realization of hyperbolic group C*-algebras as decreasing intersection of Cuntz algebras O_2

Abstract

It is proved that for every ICC group which is embeddable into a hyperbolic group, the reduced group C*-algebra is realized as the intersection of a decreasing sequence of isomorphs of the Cuntz algebra O_2. The proof is based on the study of amenable quotients of the boundary actions.

11 pages