Nonsmoothable involutions on spin 4-manifolds

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to n( − E ₈) ⊕ mH, where H is the hyperbolic form. In this paper, we prove that for n such that n ≡ 2  mod  4, there exists a locally linear pseudofree ℤ₂-action on X which is nonsmoothable with respect to any possible smooth structure on X.