  Let $\mathcal B$ be a sufficiently smooth rigid body (compact set of $\mathbb
R^3$) of arbitrary shape moving in an unbounded Navier-Stokes liquid under the
action of prescribed external force, $\textup{F}$, and torque, $\textup{M}$. We
show that if the data are suitably regular and small, and $\textup{F}$ and
$\textup{M}$ vanish for large times in the $L^2$-sense, there exists at least
one global strong solution to the corresponding initial-boundary value problem.
Moreover, this solution converges to zero as time approaches infinity. This
type of results was known, so far, only when $\mathcal B$ is a ball.
