Diffeomorphisms of odd-dimensional discs, glued into a manifold

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc identity. By classical result of Farrell and Hsiang, rational homotopy groups homology $ (D^{2n+1})$ are known in concordance stable range. We prove two results behaviour $\mu_M$ Firstly, it \emph{injective} groups, secondly, \emph{trivial} homology, if $M$ contains sufficiently many copies $S^n\times S^{n+1} \setminus int(D^{2n+1})$. The homotopical statement probably not new follows from theory torsion invariants. The homological relies work Botvinnik Perlmutter diffeomorphism odd-dimensional manifolds.