  Given a labeling c of the edges of a directed graph E by elements of a
discrete group G, one can form a skew-product graph E cross_c G. We show, using
the universal properties of the various constructions involved, that there is a
coaction delta of G on C*(E) such that C*(E cross_c G) is isomorphic to the
crossed product C*(E) cross_delta G. This isomorphism is equivariant for the
dual action deltahat and a natural action gamma of G on C*(E cross_c G);
following results of Kumjian and Pask, we show that C*(E cross_c G) cross_gamma
G is isomorphic to C*(E cross_c G) cross_{gamma,r} G, which in turn is
isomorphic to C*(E) tensor K(l^2(G)), and it turns out that the action gamma is
always amenable. We also obtain corresponding results for r-discrete groupoids
Q and continuous homomorphisms c: Q -> G, provided Q is amenable. Some of these
hold under a more general technical condition which obtains whenever Q is
amenable or second-countable.
