  We prove the Tits-Weiss conjecture for Albert division algebras over fields
of arbitrary characteristics in the affirmative. The conjecture predicts that
every norm similarity of an Albert division algebra is a product of a scalar
homothety and $U$-operators. This conjecture is equivalent to the Kneser-Tits
conjecture for simple, simply connected algebraic groups with Tits index
$E^{78}_{8,2}$. We prove that a simple, simply connected algebraic group with
Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, defined over a field of arbitrary
characteristic, is $R$-trivial, in the sense of Manin, thereby proving the
Kneser-Tits conjecture for such groups. The Tits-Weiss conjecture follows as a
consequence.
