Equivariant vector bundles over the complex projective line

Let $G$ be a finite abelian group acting faithfully on $\mathbb{C}{\mathbb{P}}^1$ via holomorphic automorphisms. In \cite{DF2} the $G$–equivariant algebraic vector bundles on $G$–invariant affine open subsets of $\mathbb{C}{\mathbb{P}}^1$ were classified. We classify the $G$–equivariant algebraic vector bundles on $\mathbb{C}{\mathbb{P}}^1$.