For a field $F$, Let $K_n(F)$ be the Quillen's $n$-th K-group of $F$.Then $K_0(F)\cong \mathbb{Z}$, $K_1(F)\cong F^\times$.
For a finite Galois extension $L/K$, $K_n(L)$ are Galois modules. Then $\mathrm{H}^1(L/K,K_0(L))=0$ trivially holds, and $\mathrm{H}^1(L/K,K_1(L))=0$ by Hilbert 90.
In Srinivas's book Algebraic K-Theory, Page 161, it is proved there if $L/K$ is a cyclic extension, then $\mathrm{H}^1(L/K,K_2(L))=0$.
For general Galois extension $L/K$, do we have $\mathrm{H}^1(L/K,K_2(L))=0$?
Do we have more Hilbert 90 style results on higher K-groups?