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.