2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65623A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the result is applied to improve some formulas in asymptotic and local cyclic cohomology of $C^*$-algebras. As an other application, it is shown that these cyclic theories are rigid after Rieffel's deformation quantizations.12pagesK-Theory and HomologyQuantum Algebra46L80text