Decomposition complexity for metric spaces was recently introduced by
Guentner, Tessera, and Yu as a natural generalization of asymptotic dimension.
We prove a vanishing result for the continuously controlled algebraic K-theory
of bounded geometry metric spaces with finite decomposition complexity. This
leads to a proof of the integral K-theoretic Novikov conjecture, regarding
split injectivity of the K-theoretic assembly map, for groups with finite
decomposition complexity and finite CW models for their classifying spaces.