Covariant representations of Hilbert C*-modules

We show that a full Hilbert C*-module X can be embedded in the multiplier module of the crossed product of X by a continuous action eta of a locally compact group G on X. Also, we show that there is a bijective correspondence between nondegenerate covariant representations of X and nondegenerate representations of the crossed product of X by eta, and moreover, this correspondence preserves the irreducibility and unitary equivalence. (C) 2012 Elsevier GmbH. All rights reserved.