A Note on Cancellation of Reflexive Modules

By the Quillen-Suslin theorem [Qui76,Sus76], we know that projective modules over a polynomial ring over a field are free. One way of saying this is, that if two projective modules of the same rank are stably isomorphic, then they are isomorphic. That, projective modules of given rank over polynomial rings are stably isomorphic was well known at the time Quillen and Suslin proved their theorems and this result is usually attributed to Grothendieck.