Geometric representations of GL(n,R), cellular Hecke algebras and the   embedding problem
  We 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. 
Uri Bader, Uri Onn