An equivariant Kastler-Kalau-Walze type theorem

In this paper, we prove an equivariant Kastler-Kalau-Walze type theorem for spin manifolds without boundary. For $6$ dimensional spin manifolds with boundary, we also give an equivariant Kastler-Kalau-Walze type theorem. Then we generalize this theorem to the general $n$ dimensional manifold. An equivariant Kastler-Kalau-Walze type theorem with torsion is also proved.