  We define a fixed point action in two-dimensional lattice CP^{N-1} models.
The fixed point action is a classical perfect lattice action, which is expected
to show strongly reduced cut-off effects in numerical simulations. Furthermore,
the action has scale invariant instanton solutions, which enables us to define
a topological charge without topological defects. We present results for the
scaling of the topological suceptibility from a Monte Carlo simulation in the
CP^3 model.
