  We give a classification of the equivariant principal $G$-bundles on a
nonsingular toric variety when $G$ is a closed Abelian subgroup of
$GL_k(\mathbb{C})$. We prove that any such bundle splits, that is, admits a
reduction of structure group to the intersection of $G$ with a torus. We give
an explicit parametrization of the isomorphism classes of such bundles for a
large family of $G$ when $X$ is complete.
