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 improve the derived version of the Torelli Theorem
for the latter surfaces already present in the litterature. We
also study the relationship between stability conditions on
projective spaces and those on their canonical
bundles.