  Let $X$ be a topological space upon which a compact connected Lie group $G$
acts. It is well-known that the equivariant cohomology $H_G^*(X;\Q)$ is
isomorphic to the subalgebra of Weyl group invariants of the equivariant
cohomology $H_T^*(X;\Q)$, where $T$ is a maximal torus of $G$. This
relationship breaks down for coefficient rings $\k$ other than $\Q$. Instead,
we prove that under a mild condition on $\k$ the algebra $H_G^*(X,\k)$ is
isomorphic to the subalgebra of $H_T^*(X,\k)$ annihilated by the divided
difference operators.
