In　the　field　of　deep　learning-based　medical　image　segmentation,　convolutional　neural　networks　(CNNs)　extract　image　features　by　combining　linear　convolutional　layers　with　nonlinear　activation　functions.　However,　excessive　stacking　of　linear　layers　in　the　network　limits　the　model＇s　ability　to　capture　fine-grained　details.　In　addition,　the　feature　distribution　imbalance　caused　by　the　traditional　fixed　grouping　strategy　(FGS)　can　affect　the　deep　model＇s　capacity　to　perceive　the　overall　structure　of　the　image.　To　address　these　challenges,　we　propose　a　medical　image　segmentation　framework,　called　Kolmogorov-Arnold　Network　with　the　adaptive　group　strategy　and　contextual　Transformer　based　on　Unet　(KAC-Unet).　First,　we　propose　the　adaptive　group　strategy　(AGS)　to　balance　the　grouping　of　different　input　channels,　alleviating　the　performance　degradation　caused　by　differences　in　group　information.　Then,　we　propose　the　Shift　Tokenized　Kolmogorov-Arnold　Network　(KAN)　Block　to　capture　complex　features　in　medical　images　through　flexible　nonlinear　transformations　and　shift　operations.　Extensive　experiments　are　conducted　on　three　medical　image　segmentation　datasets.　The　results　demonstrate　the　effectiveness　and　superiority　of　our　proposed　method　compared　with　state-of-the-art　algorithms.