### Extension of holomorphic bundles to the disc (and Serre’s Problem on Stein bundles)

Holomorphic bundles, with fiber ${\u2102}^{n}$, defined on open sets in $\u2102$ 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.