  The largest known class of gravitational backgrounds with an exact string
theoretical description is based on coset G/H CFTs and the corresponding gauged
WZW models. These backgrounds generically lack isometries and are quite
complicated. Thus the corresponding field equations seem impossible to solve
and their use in physical applications becomes problematic. We develop a
systematic general method enabling us to overcome this problem using group
theory. The method is inspired by observations made in some elementary
geometric coset and coset CFTs, but its full power is apparent in non-abelian
cases. We analyze exhaustively the coset SU(2)xSU(2)/SU(2) and explicitly solve
the scalar wave equation of the corresponding gravitational background. We also
examine the high spin limit and derive the effective geometry that consistently
captures the corresponding sector in the theory.
