  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.
