Relations Between Derived Hochschild Functors via Twisting

Let (Figure presented.) be a regular ring, and let A, B be essentially finite type (Figure presented.) -algebras. For any functor F: D(ModA) × ⋅ × D(ModA) → D(ModB) between their derived categories, we define its twist F^!: D(ModA) × ⋅ × D(ModA) → D(ModB) with respect to dualizing complexes, generalizing Grothendieck's construction of f^!. We show that relations between functors are preserved between their twists, and deduce that various relations hold between derived Hochschild (co)-homology and the f^! functor. We also deduce that the set of isomorphism classes of dualizing complexes over a ring (or a scheme) form a group with respect to derived Hochschild cohomology, and that the twisted inverse image functor is a group homomorphism.