G-Corks and Heegaard Floer homology

In [D. Auckly, H. J. Kim, P. Melvin and D. Ruberman, Equivariant corks, Algebr. Geom. Topol. 17(3) (2017) 1771-1783], Auckly-Kim-Melvin-Ruberman showed that for any finite subgroup G of SO(4) there exists a contractible smooth 4-manifold with an effective G-action on its boundary so that the twists associated to the non-trivial elements of G don't extend to diffeomorphisms of the entire manifold. We give a different proof of this phenomenon using the Heegaard Floer techniques in [S. Akbulut and Q. Karakurt, Action of the cork twist on Floer homology, in Proc. Gokova Geometry-Topology Conf. 2011 (International Press, Somerville, MA, 2012), pp. 42-52].