TITLE: Equivariant smoothing of PL structures on $S^3$
QUESTION [10 upvotes]: Suppose $S^3$ is PL sphere on which a finite group $G$ acts by PL homeomorphisms. Is it always possible to find a compatible smooth structure such that $G$ acts by diffeomorphisms?
I am not quite sure how smoothing works for trivial $G$, but maybe this can be generalized to the situation described above?

REPLY [6 votes]: The answer is "always", but it is not proven in the paper by Kwasik and Lee. They only show the existence of an equivariant smooth structure which is not necessarily compatible with the PL structure. The statement holds for manifolds up to dimension four. I tried to write a readable proof and put it on the arXiv.