  For an isotropic reductive group G satisfying a suitable rank condition over
an infinite field k, we show that the sections of the
$\mathbb{A}^1$-fundamental group sheaf of G over an extension field L/k can be
identified with the second group homology of G(L). For a split group G, we
provide explicit loops representing all elements in the
$\mathbb{A}^1$-fundamental group. Using $\mathbb{A}^1$-homotopy theory, we
deduce a Steinberg relation for these explicit loops.
