  Idempotent states on a unimodular coamenable locally compact quantum group A
are shown to be in one-to-one correspondence with right invariant expected
C*-subalgebras of A. Haar idempotents, that is, idempotent states arising as
Haar states on compact quantum subgroups of A, are characterised and shown to
be invariant under the natural action of the modular element. This leads to the
one-to-one correspondence between Haar idempotents on A and right invariant
symmetric expected C*-subalgebras of A without the unimodularity assumption.
Finally the tools developed in the first part of the paper are applied to show
that the coproduct of a coamenable locally compact quantum group restricts to a
continuous coaction on each right invariant expected C*-subalgebra.
