Nonlinearizable actions of dihedral groups on affine space

Let G be a reductive, non-abelian, algebraic group defined over C. We investigate algebraic G-actions on the total spaces of non-trivial algebraic G-vector bundles over G-modules with great interest in the case that G is a dihedral group. We construct a map classifying such actions of a dihedral group in some cases and describe the spaces of those non-linearizable actions in some examples.