2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229344We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an application we compute cohomology of some generalized Kummer varieties.A revised version: 22 pages, a new section added, typos and language errors corrected. Will appear in Revista Matematica Complutense, http://www.mat.ucm.es/serv/revmat/Algebraic Geometry14J32 (Primary); 20C10, 14F43, 14J17 (Secondary)text