Perturbation of APS boundary conditions in Lorentzian index theory

The Fredholm properties of a Lorentzian Dirac operator depend on the choice of boundary conditions that one imposes. The most relevant ones, APS boundary conditions, are well understood, but for others it is not even clear if the operator is Fredholm. We investigate how far APS boundary conditions may be perturbed whithout destroying the Fredholm properties of the Dirac operator with those boundary conditions.