Is there some reference containing an ellaboration of Morse Theory for proper actions of Lie groups? 



Morse Theory and proper actions
Have a look at



> 
> N. Hingston, *Equivariant Morse theory and closed geodesics*, 
>  J. Differential Geom.
>  Volume 19, Number 1 (1984), 1-276.
> 
> 
> 


in particular Section 2. Most statements from the equivariant Morse theory for compact group actions go over unchanged, thanks to the existence of slices for proper actions; see



> 
> R. Palais, *On the existence of slices for actions of noncompact Lie groups*,
>  Ann. of Math. 73
>  (1961)295-323.
> 
> 
> 


