In this paper we characterize the fiber representations of equivariant
complex vector bundles over a circle and classify these bundles. We also treat
the triviality of equivariant complex vector bundles over a circle by
investigating the extensions of representations. As a corollary of our results,
we calculate the reduced equivariant K-group of a circle for any compact Lie
group.Comment: 15 pages, AMS-LaTeX v1.