  Let d be a positive integer, let X be the Cantor set, and let Z^d act freely
and minimally on X. We prove that the crossed product C* (Z^d, X) has stable
rank one, real rank zero, and cancellation of projections, and that the order
on K_0 (C* (Z^d, X)) is determined by traces. We obtain the same conclusion for
the C*-algebras of various kinds of aperiodic tilings.
