  This third paper,devoted to global correspondences of Langlands,bears more
particularly on geometric-shifted bilinear correspondences on mixed (bi)motives
generated under the action of the products,right by left,of differential
elliptic operators.The mathematical frame,underlying these
correspondences,deals with the categories of the Suslin-Voevodsky mixed
(bi)motives and of the Chow mixed (bi)motives which are both in one-to-one
correspondence with the functional representation spaces of the shifted
algebraic bilinear semigroups.A bilinear holomorphic and supercuspidal spectral
representation of an elliptic bioperator is then developed.
