Essentially finite vector bundle

In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav Nori, as the main tool in the construction of the fundamental group scheme. Even if the definition is not intuitive there is a nice characterization that makes essentially finite vector bundles quite natural objects to study in algebraic geometry. So before recalling the definition we give this characterization:
Characterization.
Let formula_1 be a reduced and connected scheme over a perfect field formula_2 endowed with a section formula_3. Then a vector bundle formula_4 over formula_1 is essentially finite if and only if there exists a finite formula_2-group scheme formula_7 and a formula_7-torsor formula_9 such that formula_4 becomes trivial over formula_11 (i.e. formula_12, where formula_13).
Definition.
Let "X" be a scheme and "E" a vector bundle on "X". For formula_14 an integral polynomial with nonnegative coefficients define
A vector bundle "E" is called finite if there are two distinct polynomials "f, g" for which "f(E)" is isomorphic to "g(E)". A bundle is essentially finite if it's a subquotient of a finite vector bundle in the category of Nori-semistable vector bundles.