Homotopy invariant presheaves with framed transfers

The category of framed correspondences Fr-*(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [20]. Based on the notes [20] a new approach to the classical Morel-Voevodsky motivic stable homotopy theory was developed in [8]. This approach converts the classical motivic stable homotopy theory into an equivalent local theory of framed bispectra. The main result of the paper is the core of the theory of framed bispectra. It states that for any homotopy invariant quasi-stable radditive framed presheaf of Abelian groups F, the associated Nis-nevich sheaf F-nis, is strictly homotopy invariant and quasi-stable whenever the base field k is infinite perfect of characteristic different from 2.