On Infinite Tensor Products of Projective Unitary Representations

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.