  For complexes of modules we study two new constructions, which we call the
pinched tensor product and the pinched Hom. They provide new methods for
computing Tate homology and Tate cohomology, which lead to conceptual proofs of
balancedness of Tate (co)homology for modules over associative rings.
  Another application we consider is in local algebra. Under conditions of
vanishing of Tate (co)homology, the pinched tensor product of two minimal
complete resolutions yields a minimal complete resolution.
