  We prove that Schubert varieties are globally F-regular in the sense of Karen
Smith. We apply this result to the category of equivariant and holonomic
D-modules on flag varieties in positive characteristic. Here recent results of
Blickle are shown to imply that the simple D-modules coincide with local
cohomology sheaves with support in Schubert varieties. Using a local
Grothendieck-Cousin complex we prove that the decomposition of local cohomology
sheaves with support in Schubert cells is multiplicity free.
