  We exhibit the first examples of closed 7-dimensional Riemannian manifolds
with holonomy G_2 that are homeomorphic but not diffeomorphic. These are also
the first examples of closed Ricci-flat manifolds that are homeomorphic but not
diffeomorphic. The examples are generated by applying the twisted connected sum
construction to Fano 3-folds of Picard rank 1 and 2. The smooth structures are
distinguished by the generalised Eells-Kuiper invariant introduced by the
authors in arXiv:1406.2226.
