Using the trace formula, in 1981 James Arthur published an expression for the trace of a Hecke operator on the $L^2$ cohomology of a Hermitian locally symmetric space. Arthur and Casselman assigned us (MacPherson and myself) the homework exercise of finding a geometric interpretation, hopefully identifying Arthur's formula with the Lefschetz fixed point formula in topology. I will survey the twisted route to the solution of this problem which ultimately involved Robert Kottwitz and Guenter Harder, and which gave rise to a new cohomology theory, new expressions for discrete series characters and new combinatorics of convex cones.