Hensel's lemma for the norm principle for groups of type $D_n$

Let $G$ be a linear algebraic group defined over a field $K$. The Norm Principle for $G$ examines how the base change of $G$ to finite separable field extensions of $K$ behaves with respect to the norm map of the field extensions. It remains an open question whether the norm principle holds for all linear algebraic groups. In this talk, we will recall a Galois cohomology approach to this problem, and discuss the norm principle for groups of type $D_n$, in particular over complete discretely valued fields.