  Let $G$ be a locally compact group. Consider the C$^*$-algebra $C_0(G)$ of
continuous complex functions on $G$, tending to 0 at infinity. The product in
$G$ gives rise to a coproduct $\Delta_G$ on the C$^*$-algebra $C_0(G)$. A
locally compact {\it quantum} group is a pair $(A,\Delta)$ of a C$^*$-algebra
$A$ with a coproduct $\Delta$ on $A$, satisfying certain conditions. The
definition guarantees that the pair $(C_0(G),\Delta_G)$ is a locally compact
quantum group and that conversely, every locally compact quantum group
$(A,\Delta)$ is of this form when the underlying C$^*$-algebra $A$ is abelian.
  Assume now that $G$ is a locally compact group with a compact open subgroup
$K$. The algebra of complex functions on $G$ of {\it polynomial type} is a
dense multiplier Hopf $^*$-algebra with positive integrals (i.e. an algebraic
quantum group}. The characteristic function of $K$ is a group-like projection
in this algebraic quantum group.
  In this paper, we study group-like projections in an arbitrary algebraic
quantum group. We find several associated objects that generalize the classical
objects associated to a compact open subgroup of a locally compact group.
