  A p-compact group, as defined by Dwyer and Wilkerson, is a purely
homotopically defined p-local analog of a compact Lie group. It has long been
the hope, and later the conjecture, that these objects should have a
classification similar to the classification of compact Lie groups.
  In this paper we finish the proof of this conjecture, for p an odd prime,
proving that there is a one-to-one correspondence between connected p-compact
groups and finite reflection groups over the p-adic integers. We do this by
providing the last, and rather intricate, piece, namely that the exceptional
compact Lie groups are uniquely determined as p-compact groups by their Weyl
groups seen as finite reflection groups over the p-adic integers. Our approach
in fact gives a largely self-contained proof of the entire classification
theorem.
