Equality of linear and symplectic orbits

It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring in which 2 is invertible is identical with the set of orbits of the action of the corresponding elementary transvection group. This result is used to get improved injective stability estimates for K1K1 of the symplectic transvection group over a non-singular affine algebras.