  We consider quantum group representations for a semisimple algebraic group G
at a complex root of unity q. Here q is allowed to be of any order. We revisit
some fundamental results of Parshall-Wang and Andersen-Polo-Wen from the 90's.
In particular, we show that the category Rep(G_q) of quantum group
representations has enough projectives and injectives, and that a
G_q-representation is projective (resp. injective) if and only if its
restriction to the small quantum group is projective (resp. injective). Our
results reduce to an analysis of the Steinberg representation in the
simply-connected setting, and are well-known at odd order q via works of the
aforementioned authors. The details at arbitrary q have, to our knowledge, not
appeared in the literature up to this point.
