O A ] 9 J un 2 00 3 K-duality for pseudomanifolds with isolated singularities

We associate to a pseudomanifold X with a conical singularity a differentiable groupoid G which plays the role of the tangent space of X. We construct a Dirac element and a Dual Dirac element which induce a K-duality between the C∗-algebras C∗(G) and C(X). This is a first step toward an index theory for pseudomanifolds.