  The category of strict polynomial functors inherits an internal tensor
product from the category of divided powers. To investigate this monoidal
structure, we consider the category of representations of the symmetric group
which admits a tensor product coming from its Hopf algebra structure. It is
classical that there exists a functor F from the category of strict polynomial
functors to the category of representations of the symmetric group. Our main
result is that this functor F is monoidal. In addition we study the relations
under F between projective strict polynomial functors and permutation modules
and the link to symmetric functions.
