My coauthors and I are writing a paper based on MO questions and answers: Friedrich Knop's answer, my answer 1 and my answer 2. For a linear algebraic group $G$ over a perfect field $k$, I consider a cohomology class $\xi\in H^1(k,G)$. For a finite extension $K/k$, I consider the image of $\xi$ in $H^1(K,G)$, the restriction of $\xi$ to the smaller Galois group.

Question.Is there a standard notation for the image in $H^1(K,G)$ of $\xi\in H^1(k,G)$ ? Is it ${\rm Res}_k^K(\xi)$ or ${\rm Res}_K^k(\xi)$ ?

If there is no standard notation, I would be grateful for suggestions of *reasonable* notation.