Rigidity theorem for presheaves with Witt-transfers

The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth schemes over a field $k$ of characteristic different form two is proved. Namely, for any such sheaf $F$, isomorphism $\mathcal F(U)\simeq \mathcal F(x)$ is established, where $U$ is an essentially smooth local Henselian scheme with a separable residue field over $k$. As a consequence, the rigidity theorem for the presheaves $W^i(-\times Y)$ for any smooth $Y$ over $k$ is obtained, where the $W^i(-)$ are derived Witt groups. Note that the result of the work is rigidity with integral coefficients. Other known results are state isomorphisms with finite coefficients.