We show that every closed, simply connected, spin topological –manifold except and admits a homologically trivial, pseudofree, locally linear action of for any sufficiently large prime number which is nonsmoothable for any possible smooth structure.
"Nonsmoothable group actions on spin $4$–manifolds." Algebr. Geom. Topol. 11 (3) 1345 - 1359, 2011. https://doi.org/10.2140/agt.2011.11.1345