2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58550We 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.21 pages, Latex; updated version with few slight changes, some Comments have been deleted. Rocky Mountain J. Math., to appearOperator AlgebrasFunctional AnalysisRepresentation Theory22D10, 22D25, 46L55, 43A07, 43A65text