  Let $X$ be a complete toric variety equipped with the action of a torus $T$
and $G$ a reductive algebraic group, defined over an algebraically closed field
$K$. We introduce the notion of a compatible $\Sigma$--filtered algebra
associated to $X$, generalizing the notion of a compatible $\Sigma$--filtered
vector space due to Klyachko, where $\Sigma$ denotes the fan of $X$. We combine
Klyachko's classification of $T$--equivariant vector bundles on $X$ with Nori's
Tannakian approach to principal $G$--bundles, to give an equivalence of
categories between $T$--equivariant principal $G$--bundles on $X$ and certain
compatible $\Sigma$--filtered algebras associated to $X$, when the
characteristic of $K$ is $0$.
