Extension of holomorphic bundles to the disc (and Serre's problem on Stein bundles)

Holomorphic bundles, with fiber C-n, defined on open sets in C by locally constant transition automorphisms, are shown to extend to holomorphic bundles on the Riemann sphere. In particular, it allows us to give an example of a non-Stein holomorphic bundle on the unit disc, with polynomial transition automorphisms.