  To each natural star product on a Poisson manifold $M$ we associate an
antisymplectic involutive automorphism of the formal neighborhood of the zero
section of the cotangent bundle of $M$. If $M$ is symplectic, this mapping is
shown to be the inverse mapping of the formal symplectic groupoid of the star
product. The construction of the inverse mapping involves modular automorphisms
of the star product.
