  The framework of dynamical C*-algebras for scalar fields in Minkowski space,
based on local scattering operators, is extended to theories with locally
perturbed kinetic terms. These terms encode information about the underlying
spacetime metric, so the causality relations between the scattering operators
have to be adjusted accordingly. It is shown that the extended algebra
describes scalar quantum fields, propagating in locally deformed Minkowski
spaces. Concrete representations of the abstract scattering operators, inducing
this motion, are known to exist on Fock space. The proof that these
representers also satisfy the generalized causality relations requires,
however, novel arguments of a cohomological nature. They imply that Fock space
representations of the extended dynamical C*-algebra exist, involving linear as
well as kinetic and pointlike quadratic perturbations of the field.
