COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS

Consider a projective limit G of finite groups G, Fix a compatible family delta(n) of coactions of the G(n) on a C*-algebra A. From this data we obtain a coaction delta of G on A. We show that the coaction crossed product of A by 3 is isomorphic to a direct limit of the coaction crossed products of A by the delta(n). If A = C*(Lambda) for some k-graph Lambda, and if the coactions delta(n) correspond to skew-products of Lambda, then we can say more. We prove that the coaction crossed product of C*(Lambda) by delta may be realized as a full corner of the C*-algebra of a (k + 1)-graph. We then explore connections with Yeend's topological higher-rank graphs and their C*-algebras.