  We describe the equivariant cohomology ring of rationally smooth projective
embeddings of reductive groups. These embeddings are the projectivizations of
reductive monoids. Our main result describes their equivariant cohomology in
terms of roots, idempotents, and underlying monoid data. Also, we characterize
those embeddings whose equivariant cohomology ring is obtained via restriction
to the associated toric variety. Such characterization is given in terms of the
closed orbits.
