Absolutely split real algebraic vector bundles over a real form of projective space

Let M be a projective variety, defined over the field of real numbers, with the property that the base change M×RC is isomorphic to CPN for some N. A real algebraic vector bundle E over M will be called absolutely split if the vector bundle E⊗RC over M×RC splits into a direct sum of line bundles. We classify the isomorphism classes of absolutely split vector bundles over M.