  This paper extends the notion of geometric control in algebraic K-theory from
additive categories with split exact sequences to other exact structures. In
particular, we construct exact categories of modules over a Noetherian ring
filtered by subsets of a metric space and sensitive to the large scale
properties of the space. The algebraic K-theory of these categories is related
to the bounded K-theory of geometric modules of Pedersen and Weibel the way
G-theory is classically related to K-theory. We recover familiar results in the
new setting, including the nonconnective bounded excision and equivariant
properties. We apply the results to the G-theoretic Novikov conjecture which is
shown to be stronger than the usual K-theoretic conjecture.
