A family of theories which interpolate between vector and chiral Schwi
nger models is studied on the two-sphere S2. The conflict between the
loss of gauge invariance and global geometrical properties is solved b
y introducing a fixed background connection. In this way the generaliz
ed Dirac-Weyl operator can be globally defined on S2. The generating f
unctional of the Green functions is obtained by taking carefully into
account the contribution of gauge fields with non-trivial topological
charge and of the related zero-modes of the Dirac determinant. In the
decompactification limit, the Green functions of the flat case are rec
overed; in particular the fermionic condensate in the vacuum vanishes,
at variance with its behaviour in the vector Schwinger model.