  The action of the total cohomology $H^*(M)$ of the almost Kahler manifold $M$
on its Floer cohomology, int roduced originally by Floer, gives a new ring
structure on $H^*(M)$. We prove that the total cohomology space $H^* (M)$,
provided with this new ring structure, is isomorphic to the quantum cohomology
ring. As a special case, we prove the the formula for the Floer cohomology ring
of the complex grassmanians conjectured by Vafa and Witten.
