On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)

Abstract

We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 and E78 8,2. As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type 1E6.