  The CP symmetry is a fundamental discrete symmetry in chiral gauge theory.
Therefore this symmetry is expected to be kept also on the lattice. However, it
has been pointed out by Hasenfratz that the chiral fermion action in Luscher's
formulation of lattice chiral gauge theory is not invariant under CP
transformation. In this thesis, we first review the method of constructing
chiral gauge theory on the lattice. Then we generalize the analysis of
Hasenfratz and show that CP symmetry is not manifestly implemented for the
local and doubler-free Ginsparg-Wilson operator under rather general
assumptions for chiral projection operators. We next calculate the fermion
generating functional and precisely identify where the effects of this CP
breaking appear in this formulation. The basics of lattice gauge theory are
briefly summarized in Appendix.A.
