2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138987We introduce the notion of strong Morita equivalence for group actions on locally C*-algebras and prove that the crossed products associated with two strongly Morita equivalent continuous inverse limit actions of a locally compact group G on the locally C*-algebras A and B are strongly Morita equivalent. This generalizes a result of F. Combes, Proc. London Math. Soc. 49(1984) and R. E. Curto, P.S. Muhly, D. P. Williams, Proc. Amer. Soc. 90(1984).25 pages, presented at: ICM 2006, Section "Operator Algebras and Functional Analysis, minor correctionsOperator AlgebrasFunctional Analysis46L08, 46L05, 46L55text