We shall consider a locally compact groupoid endowed with a Haar system ν and having proper orbit space. We shall associate to each appropriate cross section σ :G⁽⁰⁾ → G^F for d_F:G^F→ G⁽⁰⁾ (where F is a Borel subset of G⁽⁰⁾ meeting each orbit exactly once) a C^*-algebra M_σ ^*( G,ν ) . We shall prove that the C^*-algebras associated with different Haar systems are *-isomorphic.

This work was partly supported by the MEC-CNCSIS grant At127/2004 and by the Postdoctoral Training Program HPRN-CT-2002-0277.