  We show that standard cyclic actions on Brieskorn homology 3-spheres with
non-empty fixed set do not extend smoothly to any contractible smooth
4-manifold it may bound. The quotient of any such extension would be an acyclic
$4$-manifold with boundary a related Brieskorn homology sphere. We briefly
discuss well known invariants of homology spheres that obstruct acyclic
bounding 4-manifolds, and then use a method based on equivariant Yang-Mills
moduli spaces to rule out extensions of the actions.
