  One of the first remarkable results in the representation theory of artin
algebras, due to Auslander and Ringel-Tachikawa, is the characterization of
when an artin algebra is representation-finite. In this paper, we investigate
aspects of representation-finiteness in the general context of exact categories
in the sense of Quillen. In this framework, we introduce "big objects" and
prove an Auslander-type "splitting-big-objects" theorem. Our approach
generalises and unifies the known results from the literature. As a further
application of our methods, we extend the theorems of Auslander and
Ringel-Tachikawa to arbitrary dimension, i.e. we characterise when a
Cohen-Macaulay order over a complete regular local ring is of finite
representation type.
