Strange actions of groups on spheres (Q1073400)

For r sufficiently large we construct actions of generalized dihedral groups (free of rank r)\(\rtimes {\mathbb{Z}}_ 2\) on \(S^ 3\) which are discrete, smooth, uniformly quasiconformal, but which are not topologically conjugate to conformal actions. This is at odds with the situation for actions on \(S^ 2\). This and other wild analogs of Schottky actions are considered.