  Recently we have discussed realization of an exact chiral symmetry in
theories with self-interacting fermions on the lattice, based upon an auxiliary
field method. In this paper we describe construction of the lattice chiral
symmetry and discuss its structure in more detail. The antifield formalism is
used to make symmetry consideration more transparent. We show that the quantum
master equation in the antifield formalism generates all the relevant
Ward-Takahashi identities including a Ginsparg-Wilson relation for interacting
theories. Solutions of the quantum master equation are obtained in a closed
form, but the resulting actions are found to be singular. Canonical
transformations are used to obtain four types of regular actions. Two of them
may define consistent quantum theories. Their Yukawa couplings are the same as
those obtained by using the chiral decomposition in the free field algebra.
Inclusion of the complete set of the auxiliary fields is briefly discussed.
