What is the status of the Schoenflies problem in the PL category? In other words, given an injective PL map $f:S^{n-1} \hookrightarrow S^n$, is it always PL equivalent to the equatorial inclusion? (I know the problem is still open for $n=3$.) Relatedly, is it true that a codimension one injective map of closed PL manifolds is always locally flat?  Also, relatedly, does topological locally flatness imply PL locally flatness in codimension one?