Geodesic
The maintenance of homotopy invariance for presheaves with Witt-transfers under Nisnevich sheafication
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 113-125

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In the present paper, we introduce a category $Wor$, whose objects are affine smooth varieties over a field $k$ and morphisms are a certain variant of finite correspondences. A presheaf of abelian groups with Witt-transfers is by definition a presheaf of abelian groups on the category $Wor$. We prove the homotopy invariance of the Nisnevich sheaf associated with an arbitrary homotopy invariant presheaf with Witt-transfers. To construct a category of Witt-motives one should prove the homotopy invariance of Nisnevich cohomology of an arbitrary homotopy invariant Nisnevich sheaf with Witt-transfers. 
@article{ZNSL_2014_423_a5,
     author = {A. E. Druzhinin},
     title = {The maintenance of homotopy invariance for presheaves with {Witt-transfers} under {Nisnevich} sheafication},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--125},
     publisher = {mathdoc},
     volume = {423},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a5/}
}
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A. E. Druzhinin. The maintenance of homotopy invariance for presheaves with Witt-transfers under Nisnevich sheafication. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 113-125. http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a5/