Grothendieck-Witt groups of henselian valuation rings

We compute higher Grothendieck-Witt groups of henselian discrete valuation rings. More specifically, we demonstrate that, when taken with finite coefficients, the corresponding Grothendieck-Witt functors send the canonical residue maps to isomorphisms. In the first part of the manuscript this property is verified for symplectic K -theory. For this aim modified methods of Suslin are employed. Subsequently, by applying Karoubi's induction, the result is extended to all higher Grothendieck-Witt groups. The utilization of the universal homotopy method enables us to address the case of mixed characteristics.