Let G denote a connected reductive algebraic group over an algebraically closed field k and let X denote a projective G × G -equivariant embedding of G . The large Schubert varieties in X are the closures of the double cosets BgB , where B denotes a Borel subgroup of G , and g ε G . We prove that these varieties are globally F -regular in positive characteristic, resp. of globally F -regular type in characteristic 0. As a consequence, the large Schubert varieties are normal and Cohen-Macaulay.