  Recent measurements of B^0 -> pi pi decays reveal two features that are in
conflict with conventional calculations: the channel B^0 (Bbar^0) -> pi^+ pi^-
shows a large direct CP-violating asymmetry, and the channel B^0 (B^0) -> pi^0
pi^0 has an unexpectedly high branching ratio. We show that both features can
be understood in terms of strong-interaction mixing of pi pi and D Dbar
channels in the isospin-zero state, an effect that is important because of the
large experimentally observed ratio Gamma(B^0 / Bbar^0 -> D^+ D^-) / Gamma (B^0
/ Bbar^0 -> pi^+ pi^-) approx. 50. Our dynamical model correlates the branching
ratios and the CP-violating parameters C and S, for the decays B^0 (Bbar^0) ->
pi^+ pi^-, B^0 (Bbar^0) -> pi^0 pi^0, B^0 (Bbar^0) -> D^+ D^- and B^0 (Bbar^0)
-> D^0 Dbar^0.
