Let $\mathrm {F}$ be a nonarchimedean locally compact field of residue characteristic $p$, let $\mathrm {D}$ be a finite dimensional central division $\mathrm {F}$-algebra and let $\mathrm {R}$ be an algebraically closed field of characteristic different from $p$. To any irreducible smooth representation of $\mathrm {G}=\mathrm {GL}_m(\mathrm {D})$, $m\>1$ with coefficients in $\mathrm {R}$, we can attach a uniquely determined inertial of supercuspidal pairs of $\mathrm {G}$. This provides us with a partition of the set of all isomorphism es of irreducible representations of $\mathrm {G}$. We write $\mathscr {R}(\mathrm {G})$ for the category of all smooth representations of $\mathrm {G}$ with coefficients in $\mathrm {R}$. To any inertial $\Omega$ of supercuspidal pairs of $\mathrm {G}$, we can attach the subcategory $\mathscr {R}(\Omega )$ made of smooth representations all of whose irreducible subquotients are in the subset determined by this inertial . We prove that the category $\mathscr {R}(\mathrm {G})$ decomposes into the product of the $\mathscr {R}(\Omega )$'s, where $\Omega$ ranges over all possible inertial of supercuspidal pairs of $\mathrm {G}$, and that each summand $\mathscr {R}(\Omega )$ is indecomposable.