  Let G be a reductive algebraic group associated to a self-adjoint homogeneous
cone defined over Q, and let G' be an appropriate neat arithmetic subgroup of
G. We present two algorithms to compute the action of the Hecke operators on
the integral cohomology of G'. This simultaneously generalizes the modular
algorithm of Ash-Rudolph to a larger class of groups, and provides techniques
to compute the Hecke-module structure of previously inaccessible cohomology
groups.
