2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61252Let A a k-algebra, H a Hopf algebra, E = A#H a general crossed product and M an E-bimodule. We obtain a complex simpler than the canonical one, giving the Hochschild homology of E with coefficients in M. This complex is eqquiped with a natural filtration. We prove that the associated spectral sequence coincides with that obtained by either, the Hochschild-Serre direct method or the Cartan-Leray-Grothendieck method. We also get similar results for the cohomology.26 pagesK-Theory and HomologyRings and Algebras16E40; 16W30text