  Let $SL_{2n}$, $Sp_{2n}$, $E_6 = G^{sc}(E_6)$, $F_4 = G(F_4)$ be simply
connected split algebraic groups over an arbitrary field $F$. Algebraic
K-theory of affine homogeneous varieties $SL_{2n}/Sp_{2n}$ and $E_6/F_4$ is
computed. Moreover, explicit elements that generate $K_*(SL_{2n}/Sp_{2n})$ and
$K_*(E_6/F_4)$ as $K_*(F)$-algebras are provided. For some twisted forms of
these varieties K-theory is also computed.
