  We address the computation of the determinant for the Dirac operator
corresponding to a quark propagating in a background gluon field of the
following type: the gauge field is covariantly constant and self-dual inside a
hypersphere and with quark fields satisfying bag-like (chiral-violating)
boundary conditions at the surface of the hypersphere. We find that the parity
odd part of the logarithm of the determinant corresponds to the Abelian
anomaly. However the parity even part also depends on the chiral angle
associated with the boundary. This unexpected dependence is discussed.
