Standard (GL) Hall polynomials (1) count the number of filtrations of an abelian p-group with given subfactors, (2) count the number of partial flags over F_p respecting (in some sense) a given nilpotent operator, (3) give the structure constants of the Hecke algebra of GL (N, F_p) in a natural basis. Incarnations (2) and (3) allow straightforward generalizations to arbitrary reductive groups. I'll describe a generalization of (1). As a corollary I'll sketch a new geometric realization of the tensor category of finite dimensional representations of a reductive group.