Chernousov–Gille–Pianzola conjecture on Zariski-locally trivial torsors

Let $k$ be a field of characteristic $0$, let $R=k[x_1^{\pm 1},\ldots,x_n^{\pm 1}]$, and let $G$ be a loop reductive group over $R$, meaning that $G$ contains a maximal $R$-torus. Assume that all semisimple quotients of $G$ are isotropic, meaning that they contain $\operatorname{\mathbf G}_m{}_R$. Chernousov–Gille–Pianzola conjecture. The Zariski cohomology set

$$H^1_{Zar}(R,G)$$

is trivial. The conjecture concerns the classification of Zariski-locally trivial torsors for loop reductive groups over Laurent polynomial rings; the source paper states that it is settled affirmatively.