  Local $\alpha \alpha$ potentials fail to describe $^{12}$C as a $3\alpha$
system. Nonlocal $\alpha \alpha$ potentials that renormalize the
energy-dependent kernel of the resonating group method allow interpreting
simultaneously the ground state and $0^+_2$ resonance of $^{12}$C as $3\alpha$
states. A comparison with fully microscopic calculations provides a measure of
the importance of three-cluster exchanges in those states.
