  We establish a one to one correspondence between idempotent states on a
locally compact quantum group G and integrable coideals in the von Neumann
algebra of bounded measurable functions on G that are preserved by the scaling
group. In particular we show that there is a 1-1 correspondence between
idempotent states on G and psi-expected left invariant von Neumann subalgebras
of bounded measurable functions on G. We characterize idempotent states of Haar
type as those corresponding to integrable normal coideals preserved by the
scaling group. We also establish a one to one correspondence between open
subgroups of G and convolutionally central idempotent states on the dual of G.
Finally we characterize coideals corresponding to open quantum subgroups of G
as those that are normal and admit an atom. As a byproduct of this study we get
a number of universal lifting results for Podles condition, normality and
regularity and we generalize number of results known before to hold under the
coamenability assumption.
