Title: Group-like projections for locally compact quantum groups,
Abstract: Let $\mathbb{G}$ be a locally compact quantum group. We give a 1-1
correspondence between group-like projections in $L^\infty(\mathbb{G})$
preserved by the scaling group and idempotent states on the dual quantum group
$\widehat{\mathbb{G}}$. As a byproduct we give a simple proof that normal
integrable coideals in $L^\infty(\mathbb{G})$ which are preserved by the
scaling group are in 1-1 correspondence with compact quantum subgroups of
$\mathbb{G}$.