  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
$\mathrm{E}_{7,1}^{78}, \mathrm{E}_{8,2}^{78}$. 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 $^1\mathrm{E}_6$.
