In this article we present a fundamental result due to Sumihiro. It states that every normal G-variety X, where G is a connected linear algebraic group, is locally isomorphic to a quasi-projective G-variety, i.e., to a G-stable subvariety of the projective space P n with a linear G-action (Theorem 1.1). The central tools for the proof are G-linearization of line bundles (§2) and some properties of the Picard group of a linear algebraic group (§4).