a semisimple (more generally, reductive) group scheme is called isotropic, if it contains a proper parabolic subgroup. in particular, the special orthogonal group of a non-degenerate quadratic form is isotropic if and only if the form itself is isotropic. to any isotropic reductive group g over a commutative ring r one associates a group-valued functor $k_1^g$ on the category of commutative r-algebras, which is an analog of the non-stable $k_1-functor gl_n/e_n$. when r is a field, $k_1^g$ coincides on smooth algebras with the group of $a^1$-connected components of g in the sense of morel-voevodsky. we will discuss various properties of these functors, and connections with classification of principal g-bundles.