  The construction and analysis of deformations of quantum field theories by
warped convolutions is extended to a class of globally hyperbolic spacetimes.
First, we show that any four-dimensional spacetime which admits two commuting
and spacelike Killing vector fields carries a family of wedge regions with
causal properties analogous to the Minkowski space wedges. Deformations of
quantum field theories on these spacetimes are carried out within the
operator-algebraic framework - the emerging models share many structural
properties with deformations of field theories on flat spacetime. In
particular, deformed quantum fields are localized in the wedges of the
considered spacetime. As a concrete example, the deformation of the free Dirac
field is studied. Second, quantum field theories on de Sitter spacetime with
global U(1) gauge symmetry are deformed using the joint action of the internal
symmetry group and a one-parameter group of boosts. The resulting theories turn
out to be wedge-local and non-isomorphic to the initial one for a class of
theories, including the free charged Dirac field. The properties of deformed
models coming from inclusions of CAR-algebras are studied in detail. Third, the
deformation of the scalar free field in the Araki-Wood representation on
Minkowski spacetime is discussed as a motivating example.
