The norm principle for type $D_n$ groups over complete discretely valued fields

Let $K$ be a complete discretely valued field with residue field $k$ with $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(k)\mathrm{\ne }2$. Assuming that the norm principle holds for extended Clifford groups $\mathrm{\Omega }(q)$ for every even dimensional non-degenerate quadratic form $q$ defined over any finite extension of $k$, we show that it holds for extended Clifford groups $\mathrm{\Omega }(Q)$ for every even dimensional non-degenerate quadratic form $Q$ defined over $K$.