The gravitational chiral anomaly of the spin-1/2 field in the presence of twisted boundary conditions for ordinary field theory

We calculate the chiral anomaly in the neighborhood of the fixed point spac e cal M-h which is constructed by the group action of a discrete symmetry h on a compact manifold cal M. The Feynman diagrams approach for the corresp onding supersymmetric quantum mechanical system with twisted boundary condi tions is used. The result we derive in this way agrees with the generalizat ion of the ordinary index theorem (the G-index theorem) on the spin complex .