On the splitting principle for cohomological invariants of reflection groups

Abstract: Let $\mathrm{k}{0}$ be a field and $W$ a finite orthogonal reflection group over $\mathrm{k}{0}$. We prove Serre's splitting principle for cohomological invariants of $W$ with values in Rost's cycle modules (over $\mathrm{k}{0}$) if the characteristic of $\mathrm{k}{0}$ is coprime to $|W|$. We then show that this principle for such groups holds also for Witt- and Milnor-Witt $K$-theory invariants.