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For any second countable locally compact group G, we construct a simpleG-C*-algebra whose full and reduced crossed product norms coincide. We thenconstruct its G-equivariant representation on another simple G-C*-algebrawithout the coincidence condition. This settles two problems posed byAnantharaman-Delaroche in 2002. Some constructions involve the Baire categorytheorem.

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