Nonlinearizable actions of dihedral groups on affine space

Let be a reductive, non-abelian, algebraic group defined over . We investigate algebraic -actions on the total spaces of non-trivial algebraic -vector bundles over -modules with great interest in the case that 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.