Title: Equivariant Bismut Laplacian and spectral Einstein functional

Abstract: This paper aims to provide an explicit computation of the equivariant noncommutative residue density of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. A considerable contribution of this paper is the development of the spectral Einstein functionals by two vector fields and the equivariant Bismut Laplacian over spinor bundles. We prove the equivariant Dabrowski-Sitarz-Zalecki type theorems for lower dimensional spin manifolds with (or without) boundary.