Equivariant Corks
  For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on $\partial C$ whose associated pairs (C,g) for all $g \in G$ are distinct smoothings of the pair $(C,\partial C)$. Indeed C embeds in a 4-manifold so that cutting out C and regluing using distinct elements of G yield distinct smooth 4-manifolds. 
Dave Auckly, Hee Jung Kim, Paul Melvin, Daniel Ruberman
math.GT