  We introduce the Hopf algebra of uniform block permutations and show that it
is self-dual, free, and cofree. These results are closely related to the fact
that uniform block permutations form a factorizable inverse monoid. This Hopf
algebra contains the Hopf algebra of permutations of Malvenuto and Reutenauer
and the Hopf algebra of symmetric functions in non-commuting variables of
Gebhard, Rosas, and Sagan.
