GRASSMANNIAN AND CHIRAL ANOMALY

We discuss the Grassmannian of self-adjoint global elliptic boundary c onditions with gamma(5)- and gauge-invariance of the domain for the Di rac operator over the 4-ball coupled to a gauge configuration with non -trivial curvature form. We show that this space contains a variety of boundary conditions in addition to the spectral Atiyah-Patodi-Singer projection and that some of them, like the Calderon projector, imply t he vanishing of the index of the Dirac operator and therefore the inva riance of the fermion determinant under global (i.e. rigid) chiral tra nsformations.