Twisted Group Algebras, Normal Subgroups and Derived Equivalences

We study Rickard equivalences between p-blocks of twisted group algebras and their local structure, in connection with Dade's conjectures. We prove that an extended form of Broué's conjecture implies Dade's Inductive Conjecture in the Abelian defect group case; this is a consequence of the fact that Rickard equivalences induced by complexes of graded bimodules preserve the relevant Clifford theoretical invariants. As an application, we show that these conjectures hold for p-extensions of blocks with cyclic defect groups.