  Given a discrete group $\Gamma$ of isometries of a negatively curved manifold
$\widetilde M$, a nontrivial conjugacy class $\mathfrak K$ in $\Gamma$ and
$x_0\in\widetilde M$, we give asymptotic counting results, as $t\to +\infty$,
on the number of orbit points $\gamma x_0$ at distance at most $t$ from $x_0$,
when $\gamma$ is restricted to be in $\mathfrak K$, as well as related
equidistribution results. These results generalise and extend work of Huber on
cocompact hyperbolic lattices in dimension $2$. We also study the growth of
given conjugacy classes in finitely generated groups endowed with a word
metric.
