  We report the results from a study of the full sample of ~ 6.031 10^7 K+- ->
pi+- pi0 pi0 decays recorded by the NA48/2 experiment at the CERN SPS. As first
observed in this experiment, the pi0 pi0 invariant mass M00 distribution shows
a cusp-like anomaly in the region around M00 = 2m+, where m+ is the charged
pion mass. This anomaly has been interpreted as an effect due mainly to the
final state charge exchange scattering process pi+ pi- -> p0 p0 in K+- -> pi+-
pi+ pi- decay. Fits to the M00 distribution using two different theoretical
formulations provide the presently most precise determination of (a0 - a2), the
difference between the pi pi S-wave scattering lengths in the isospin I=0 and
I=2 states. Higher-order pi pi rescattering terms, included in the two
formulations, allow also an independent, though less precise, determination of
a2.
