We construct a non-atomic strong operator topology-dense probability measure on the set of unitary operators acting on a separable Hilbert space, such that the $C^∗$-algebra generated by $n ≥ 3$ independently chosen random unitaries is almost surely non-exact.
Bernhard Burgstaller. "The exactness of certain randomized C∗-algebras." Illinois J. Math. 55 (3) 963 - 976, Fall 2011. https://doi.org/10.1215/ijm/1369841793