Equivariant Twisted Bismut Laplacian with Torsion and KKW type theorems

This paper aims to provide an explicit computation of the noncommutative residue density associated with equivariant twisted Bismut Laplacian with torsion on compact manifolds with (or without) boundary. We prove the equivariant twisted Kastler-Kalau-Walze type theorems with torsion on compact manifolds with boundary.