Quillen's question on projective modules over a punctured regular local ring

Let $R$ be a regular local ring with maximal ideal $m$, and let $f\in m\setminus m^2$. Quillen's question. Every finitely generated projective $R_f$-module is free.

This is the module-theoretic predecessor and motivating special case of Nisnevich's conjecture; the source presents it as Quillen's question rather than explicitly assigning it a resolution status.