  We prove that linear groups over rings of non-commutative Laurent polynomials
$D_{\tau}$ have Tits systems with the corresponding affine Weyl groups and have
universal central extensions if $|Z(D)|\geq 5$ and $|Z(D)|\neq 9$. We also
determine structures of $K_1$-groups and identify generators of $K_2$-groups.
