CP, T and CPT in the non-perturbative formulation of chiral gauge theories

In spite of significant recent progress on the non-perturbative formulation of chiral gauge theories there remained several unsolved problems. One of them is the puzzle that the left- and right-handed projectors, and so the left- and right-handed actions, break CP-symmetry on the lattice. We show in this Letter that they break T-symmetry also, while CPT remains intact.