The Hopf algebroids of functions on etale groupoids and their principal Morita equivalence

We show that the bimodules associated to the maps between etale groupoids admit a natural cocommutative coalgebra structure which is preserved under composition. Moreover, we obtain a Hopf algebroid structure on the Connes convolution algebra of an etale groupoid, which is invariant under Morita-equivalence. (C) 2001 Elsevier Science B.V. Air rights reserved.