Joint work with S. Alsaody and A. Pianzola. In the first part of the talk we remind the definition of an R-equivalence (introduced by Manin), state the Tits-Weiss conjecture on generation of structure groups of Albert algebras by U-operators and the Kneser-Tits conjecture for isotropic groups. In the second part of the talk we focus on computation of R-equivalence classes for groups of type E_6. As corollaries of our result we prove the Tits-Weiss conjecture and the Kneser-Tits conjecture for some isotropic groups of type E_7 and E_8.