A cancellation theorem for projective modules over affine algebras over C1-fields

Let k be a C1-field of characteristic zero. Let Abe an affine algebra of dimension d 2 over k. In this set up, Suslin proved that the free module Ad is cancellative (in other words, stably free A-modules of rank d are free). In this note we show that, in fact, all finitely generated projective A-modules of rank d arecancellative.