It is well known that the moduli space of flat connections on a trivial
principal bundle MxG, where G is a connected Lie group, is isomorphic to the
representation variety Hom(\pi_1(M), G)/G. For a tiling T, viewed as a marked
copy of R^d, we define a new kind of bundle called pattern equivariant bundle
over T and consider the set of all such bundles.