  Let $n$ be a positive integer and $q$ a prime power. We prove that a refined
version of Brou\'{e}'s abelian defect group conjecture holds for unipotent
$\ell$-blocks of ${\rm GL}_n(q)$, where $\ell\nmid q$. We also give a
sufficient condition on general $\ell$-blocks of ${\rm GL}_n(q)$ to satisfy the
refined abelian defect group conjecture. We explain by an example that this
sufficient condition does not hold in general.
