2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100948We study geometric representations of GL(n,R) for a ring R. The structure of the associated Hecke algebras is analyzed and shown to be cellular. Multiplicities of the irreducible constituents of these representations are linked to the embedding problem of pairs of R-modules x < y.18 pages, final version, to appear in JPAARepresentation Theory20Cxx, 13CxxGeometric representations of GL(n,R), cellular Hecke algebras and the embedding problemtext