Affine representability of quadrics revisited

The quadric Q2n is the Z-scheme defined by equation ?i=1nxiyi=z(1?z). We show that a homogeneous space for split reductive group scheme SO2n+1 over Z. known to have A1-homotopy type of motivic sphere and identification as allows us give characteristic independent affine representability statement spheres. This last observation comparison results between Chow–Witt groups, stable cohomotopy groups Euler class groups.