Diffeomorphisms of a product of spheres and embedded spheres

Let M be the product of n copies of the p-dimensional sphere Sp with p⩾1 and n⩾2. In this paper we completely determine those automorphisms of Hp(M;Z)≅Zn which can be realized by a diffeomorphism of M. As an application, we completely classify smoothly embedded p-dimensional spheres in M up to diffeomorphisms of M.