Lusztig's results mentioned above have been generalised to groups over arbitrary finite local rings, see *Unramified representations of reductive groups over finite rings*, Represent. Theory 13 (2009), 636-656.

There is a recent paper extending the above construction to certain ramified maximal tori, cf. *Extended Deligne-Lusztig varieties for general and special linear groups*, arXiv:0911.4593v1. It is shown here that the above "unramified" construction omits certain interesting representations. Some of these missing representations are connected with ramified maximal tori, and it is therefore desirable to have generalised Deligne-Lusztig varieties attached also to such tori.

In addition to the cohomological approaches to constructing representations, there are some partial purely algebraic constructions. There is a paper by G. Hill (*Regular Elements and Regular Characters of* $\text{GL}_n(\mathcal{O})$, which gives a construction of many so-called *regular* representations. These include most of the interesting representations, such as the strongly cuspidal ones.
There is also an approach, due to U. Onn, which defines a new type of induction functor (called infinitesimal induction) which complements the classical parabolic induction. This construction considers general automorphism groups of finite modules over DVRs with finite residue field. So far, this approach has led to a classification of all the representations in the rank-2 case (which includes $\text{GL}_2(\mathcal{O}/\mathfrak{p}^r)$).

Since any finite commutative ring is the direct product of finite local rings, it is enough to study representations of groups over the latter. This is however a very hard problem, and one cannot expect an explicit list of all the representations in general. As in the representation theory of most infinite groups, the most fruitful approach seems to be to define a nice category of representations which is both possible to control, and at the same time is rich enough to include most (or all) the representations one is interested in. A candidate for such a category for $\text{GL}_n(\mathcal{O})$ is the one consisting of regular representations, mentioned above. One can ask interesting questions about the regular representations, such as which of them are given by the cohomological constructions, or which of them are types for supercuspidal representations of $\text{GL}_n(F)$, where $F$ is a local field with ring of integers $\mathcal{O}$.