  We give a geometric interpretation of the Jones-Ocneanu trace on the Hecke
algebra, using the equivariant cohomology of sheaves on SL(n). This
construction makes sense for all simple algebraic groups, so we obtain a
generalization of the Jones-Ocneanu trace to Hecke algebras of other types. We
give a geometric expansion of this trace in terms of the irreducible characters
of the Hecke algebra, and conclude that it agrees with a trace defined
independently by Gomi.
  Based on our proof, we also prove that certain simple perverse sheaves on a
reductive algebraic group G are equivariantly formal for the conjugation action
of a Borel B, or equivalently, that the Hochschild homology of any Soergel
bimodule is free, as the authors had previously conjectured.
  This construction is closely tied to knot homology. This interpretation of
the Jones-Ocneanu trace is a more elementary manifestation of the geometric
construction of HOMFLYPT homology given by the authors in a previous paper.
