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We discuss heavy quarkonium production through parton fragmentation,including a review of arguments for the factorization of high-p_T particlesinto fragmentation functions for hadronic initial states. We investigate thefurther factorization of fragmentation functions in the NRQCD formalism, andargue that this requires a modification of NRQCD octet production matrixelements to include nonabelian phases, which makes them gauge invariant. Wedescribe the calculation of uncanceled infrared divergences in fragmentationfunctions that must be factorized at NNLO, and verify that they are absorbedinto the new, gauge invariant matrix elements.Comment: 53 pages latex, 37 eps files, version to appear in Phys. Rev.

Fragmentation, nonrelativistic QCD, and NNLO factorization analysis in heavy quarkonium production