  Let $k$ be an arbitrary field. The main aim of this paper is to prove the
Tits-Weiss conjecture for Albert division algebras over $k$ which are pure
first Tits constructions. This conjecture asserts that for an Albert division
algebra $A$ over a field $k$, every norm similarity of $A$ is inner modulo
scalar multiplications. It is known that $k$-forms of $E_8$ with index
$E^{78}_{8,2}$ and anisotropic kernel a strict inner $k$-form of $E_6$
correspond bijectively (via Moufang hexagons) to Albert division algebras over
$k$. The Kneser-Tits problem for a form of $E_8$ as above is equivalent to the
Tits-Weiss conjecture (see \cite{TW}). Hence we provide a solution to the
Kneser-Tits problem for forms of $E_8$ arising from pure first Tits
construction Albert division algebras. As an application, we prove that for
$G={\bf Aut}(A),~G(k)/R=1$, where $A$ is a pure first construction Albert
division algebra over $k$ and $R$ stands for $R$-equivalence in the sense of
Manin (\cite{M}).
