TITLE: Morse Theory and proper actions
QUESTION [8 upvotes]: Is  there  some  reference  containing  an  ellaboration  of  Morse  Theory  for  proper  actions  of  Lie  groups?

REPLY [7 votes]: 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.