The Grothendieck–Serre conjecture for reductive groups

Let $R$ be a regular local ring containing a field $k$, and let $G$ be a smooth reductive algebraic group over $k$. Write $K$ for the field of fractions of $R$. Grothendieck–Serre conjecture. The natural morphism

$$H^1(R,G)\to H^1(K,G)$$

has trivial kernel.

This conjecture predicts that a $G$-torsor over a regular local ring which becomes trivial over the fraction field was already trivial over the ring. It is a central purity statement for torsors under reductive groups and is known in various cases, but the supplied source does not state a general resolution.