  Let k be a field. Let also (F, G) be a matched pair of groups. We give
necessary and sufficient conditions on a pair (\sigma, \tau) of 2-cocycles in
order that the crossed product algebra and the crossed coproduct coalgebra
k^G{}^{\tau}#_{\sigma} kF combine into a braided Hopf algebra. We also discuss
diagonal realizations of such braided Hopf algebras in the category of
Yetter-Drinfeld modules over a finite group.
