QCD splitting-function dependence on evolution variable

181 pages, 120 figures. Proceedings "Parton Radiation and Fragmentation from LHC to FCC-ee" Workshop (CERN, Nov. 2016), David d'Enterria, Peter Z. Skands (eds.)International audienceIn this note we present the results of the study performed at IFJ PAN in Krakow in thecontext of the parton-shower-related research which suggests that QCD splitting function dependson the type of physical evolution variable. We sketch a method of including NLO correctionsinto a cascade (ladder) of a parton shower (PS). The method is based on the Curci-Furmanski-Petronzio classical paper and matching between PS and NLO distributions obtained from theFeynman diagrams. We note that one does not reproduce the classical CFP NLO kernels if thekT ordering is used for the calculation. This seems to be a limitation of the denition of the CFPprocedure and requires further investigation