Let $K,L$ be finite simplicial complexes. Suppose there is a topological embedding $f: |K| \to |L|$ such that $f$ restricted to simplices of $K$ is linear (in particular $f(S)$ is completely inside a single simplex of $L$ for a simplex $S \in K$).
Is it always possible to find a subdivision of $L$, such that $f$ becomes simplicial? If not, what if $K$ and $L$ are PL-manifolds (with boundaries)? What is a good reference?