Simple algebras and algebraic groups

The following topics will be discussed:
(1) Given an algebraic group G,let V be a finite-dimensional algebraic G-module that admits a structure of a simple (not necessarily associative) algebra A for which G=Aut(A). Then V admits a close approximation to the analogue of classical invariant theory.
(2) What are the groups G for which such a V exists?
(3) Given G, what are the G-modules V for which (1) holds?