The axial anomaly of Ginsparg-Wilson fermion

The axial anomaly of Ginsparg-Wilson fermion operator D is discussed in general for the operator R which enters the chiral symmetry breaking part in the Ginsparg-Wilson relation. The axial anomaly and the index of D as well as the exact realization of the Atiyah-Singer index theorem on the lattice are determined solely by the topological characteristics of the chirally symmetric operator Dc in the chiral limit R→0.