This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I{II: the cases jaj M or axisymmetry, arXiv:1010.5132], providing the complete proof of denitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal jaj < M case without symmetry assumptions. The essential ideas of the proof (together with explicit constructions of the most dicult mul
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