  We consider the massive Klein-Gordon equation on a class of asymptotically
static spacetimes. We prove the existence and Hadamard property of the in and
out states constructed by scattering theory methods. Assuming in addition that
the metric approaches that of Minkowski space at infinity in a short-range way,
jointly in time and space variables, we define Feynman scattering data and
prove the Fredholm property of the Klein-Gordon operator with the associated
Atiyah-Patodi-Singer boundary conditions. We then construct a parametrix (with
compact remainder terms) for the Fredholm problem and prove that it is also a
Feynman parametrix in the sense of Duistermaat and H{\"o}rmander.
