I'm looking for an example, or source of examples, of a discrete uniform subgroup $G$ of a Lie group $\Gamma$, with $G$ not virtually torsion-free. By uniform subgroup I mean that the quotient $\Gamma / G$ is compact.
The furthest I have been able to get with this is that it cannot be done for simply connected soluble Lie groups - any uniform subgroup is a lattice (the quotient $\Gamma / G$ has finite volume in the Haar measure), and such lattices have matrix representations. Selberg's Lemma provides that $G$ is virtually torsion-free. (The Lemma states that a finitely generated linear group over a field of zero characteristic is virtually torsion-free.)
Any suggested references / reading would also be much appreciated, I don't know this area particularly well, so I don't really know where to look for these things.
The MathOverflow question on Uniform lattices in semisimple Lie groups contains useful information and links.
In particular, Misha Kapovich posted a comment pointing to M. S. Raghunathan, Torsion in cocompact lattices in coverings of $\operatorname{Spin}(2,n)$, Mathematische Annalen, 266 (4). pp. 403-419, where examples are constructed.