  Let G be a connected reductive group and X an equivariant compactifiction of
G. In X, we study generalised and opposite generalised Schubert varieties,
their intersections called generalised Richardson varieties and projected
generalised Richardson varieties. Any complete G-embedding has a canonical
Frobenius splitting and we prove that the compatibly split subvarieties are the
generalised projected Richardson varieties extending a result of Knutson, Lam
and Speyer to the situation.
