When X X is a finite simplicial complex and G G is any of a certain class of groups, a classification of G G -principal bundles over X X in terms of projective modules over a ring R ( G , X ) R(G,X) is given. This generalizes Swan’s classification of vector bundles and uses the results of Mulvey. Often, R R can be taken to be noetherian; in this case Spec ( R ) {\text {Spec}}(R) is usually reducible with "cohomologically trivial" irreducible components. Information is derived concerning the nature of projective modules over such rings, and some results are obtained indicating how such information reflects information about X X .