Polynomial rings and their projective modules

Let R be a regular noetherian ring. A central question concerning projective modules over polynomial R-algebras is the following. (1.1) BASS-QUILLEN CONJECTURE ([2] Problem IX, [10]). Every finitely generated projective module P over a polynomial R-algebra R[T], T = (T1,…, Tn) is extended from R, i.e. P≊R[T]⊗R P/(T)P.