Covariant representations of Hilbert C∗C∗-modules

We show that a full Hilbert C∗C∗-module XX can be embedded in the multiplier module of the crossed product of XX by a continuous action ηη of a locally compact group GG on XX. Also, we show that there is a bijective correspondence between nondegenerate covariant representations of XX and nondegenerate representations of the crossed product of XX by ηη, and moreover, this correspondence preserves the irreducibility and unitary equivalence.