Algebraic vector bundles on punctured affine spaces and smooth quadrics

There is a canonical AnAn-fibration from a (2n+1)(2n+1)-dimensional smooth affine quadric YnYn to an (n+1)(n+1)-dimensional punctured affine space XnXn. For each rank r at least n, we construct a nontrivial algebraic vector bundle of rank r   on XnXn with trivial pullback to YnYn. Moreover, we construct continuous families of arbitrarily large dimensional pairwise non-isomorphic rank n   bundles on XnXn with trivial pullbacks to YnYn.