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In 1998, Davis and Lück gave a homotopy-theoretical construction of the Baum-Connes assembly map (with trivial coefficients) using spectra over the orbit category. We construct from any G-C*-algebra A a K-theory spectrum over the orbit category and give an identification of the resulting Davis-Lück map with the classical Baum-Connes map (with coefficients in A). Our main ingredients are the localization picture of the assembly map by Meyer and Nest and a version of Green's imprimitivity theorem for C*-categories.