  We introduce a non commutative analog of the Bohr compactification. Starting
from a general quantum group G we define a compact quantum group bG which has a
universal property such as the universal property of the classical Bohr
compactification for topological groups. We study the object bG in special
cases when G is a classical locally compact group, dual of a classical group,
discrete or compact quantum group as well a quantum group arising from a
manageable multiplicative unitary. We also use our construction to give new
examples of compact quantum groups.
