  Consider a projective limit G of finite groups G_n. 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
\delta 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 realised 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.
