C*-envelopes and the Hao-Ng isomorphism for discrete groups

Using non-selfadjoint techniques, we establish the Hao-Ng isomorphism for the reduced crossed product and all discrete groups. For the full crossed product an analogous result holds for all discrete groups but the C*-correspondences involved have to be hyperrigid. These results are obtained by calculating the C*-envelope of the reduced crossed product of an operator algebra by a discrete group.