Homologically trivial linearization conjecture for cyclic actions on the complex projective plane

Let $a4n$ act smoothly on $a4cp^2$. The action is homologically trivial if it acts trivially on the second homology $H_2(a4cp^2)$. A linear action is one induced by the standard linear action on complex projective space. Homologically trivial linearization conjecture. Every homologically trivial $a4n$-action on $a4cp^2$ is smoothly equivalent to a linear action. The conjecture is known in the symplectic case and topologically, while the smooth case remains open. Nonlinear actions of $a4p\oplusa4p$ are known, but in those examples every cyclic subgroup acts linearly.