I am looking for some references on equivariant resolution of singularities. In most references quoted on mathoverflow (for instance : <https://mathoverflow.net/questions/70061/reference-on-an-equivariant-resolution-of-singularities>), they only talk about finite group action (if I am not mistaken). 

I was wondering if it is known that equivariant resolutions do not exist in general for larger group (are there counter-examples?). I am especially interested when the group is $\mathbb{C}^*$.

Thanks in advance.