The projectors of the decomposition theorem are motivated

We prove that the projectors arising from the decomposition theorem applied to a projective map of quasi-projective varieties are absolute Hodge, Andr ́e motivated, Tate and Ogus classes. As a by-product, we introduce, in characteristic zero, the notions of algebraic de Rham intersection cohomology groups of a quasi-projective variety and of intersection cohomology motive of a projective variety