Inducing stability conditions

We study stability conditions induced by functors between triangulated categories. Given a finite group acting on a smooth projective variety we prove that the subset of invariant stability conditions embeds as a closed submanifold into the stability manifold of the equivariant derived category. As an application we examine stability conditions on Kummer and Enriques surfaces and we give a derived version of the Torelli Theorem for the latter surfaces. We also study the relationship between stability conditions on projective spaces and those on their canonical bundles.