Equivariant splendid Rickard equivalences

Broué's conjecture says that if a finite group H has an abelian Sylow p-subgroup P, then the principal blocks of H   and NH(P)NH(P) are splendidly Rickard equivalent. In this paper, Broué's conjecture is reduced to simple groups with a stability condition. A structure theorem on finite groups with abelian Sylow p-subgroups, due to Kimmerle and Sandling, is used.