Let $M$ be a connected (topological) oriented $m$-manifold, and $f \colon M \to M$ a homeomorphism. Is there a locally flat oriented embedding $\Phi \colon \mathbb{D}^m \hookrightarrow M$ and an orientation preserving homeomorphism $F \colon M \to M$ such that $F$ is isotopic to $f$ and $F \Phi = \Phi$?