Simple equivariant C*-algebras whose full and reduced crossed products coincide

Abstract

For any second countable locally compact group $G$, we construct a simple $G$-C*- algebra whose full and reduced crossed product norms coincide. We then construct its $G$-equivariant representation on another simple $G$-C*-algebra without the coincidence condition. This settles two problems posed by Anantharaman-Delaroche in 2002. Some constructions involve the Baire category theorem.