I am trying to show that any group action on a type $II_1$ factor $M$ which is in standard form (i.e. acting by left multiplication on $L^2(M)$), is spatially implemented. I'm not really sure how to show this. I tried to extend the action to one on all of $B(L^2(M))$ use the fact that it is inner there and then by density of $M\Omega$ (where $\Omega$ is the cyclic vector) show that this unitary U is actually in M.
I can't get this to work. Any help would be appreciated