Construction of semi-free S3 actions on homotopy sphere with untwisted   fixed point set
  William Browder in his paper "Surgery and the theory of differentiable transformation groups" developed surgery techniques to study semi-free actions of S1 on homotopy spheres, under the additional assumption that the fixed point set is a homotopy sphere. He used this surgery to show how to construct such actions. In this paper, I discussed a similar theory for semi-free actions of S3 on homotopy spheres. An open problem is raised at the end of the paper. 
I. H. Kaddoura
math.AT