A gas turbine stator component includes a composite, segmented ring made up of an annular array of arcuate segments, each having end faces formed with respective seal slots, with radial gaps formed between opposed end faces of adjacent arcuate segments. A seal is located between each pair of opposed seal slots to thereby seal the gaps, and a channel is provided in each of said arcuate segments adapted to be supplied with cooling air, the channel connecting to a passage extending between the channel and a respective one of the seal slots or radial gaps, on a lower-pressure side of the seal.