Involved in sporophytic self-incompatibility system (the inability of flowering plants to achieve self-fertilization), probably acting in combination with S-locus-specific glycoproteins. Interaction with a ligand in the extracellular domain triggers the protein kinase activity of the cytoplasmic domain. ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] Predominantly in the pistil and anther. There are a number of different S alleles in B.oleracea, possibly providing the recognition specificity. Belongs to the protein kinase superfamily. Ser/Thr protein kinase family.