Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions

The Vafa-Witten arguments on the realization of parity and flavour symmetries in the QCD vacuum do not apply to two lattice regularizations of QCD which are able to reproduce the chiral anomaly: Wilson fermions and Ginsparg-Wilson fermions. We show here how using the last regularization one can get, from first principles, that the more standard order parameters for these symmetries take a vanishing vacuum expectation value for any number of flavours, if quarks have a non-vanishing mass.