  We initiate a study of infinite tensor products of projective unitary
representations of a discrete group G. Special attention is given to regular
representations twisted by 2-cocycles and to projective representations
associated with CCR-representations of bilinear maps. Detailed computations are
presented in the case where G is a finitely generated free abelian group. We
also discuss an extension problem about product type actions of G, where the
projective representation theory of G plays a central role.
