A gas turbine engine comprising: a compressor section (24; 101), a combustor, and a turbine section, said combustor having a radially outer surface defining a diffuser chamber radially outwardly of said combustor, said turbine section including a high pressure turbine first stage blade having an outer tip, and a blade outer air seal positioned radially outwardly of said outer tip; and a tap for tapping air having been compressed by said compressor section (24; 101) and being passed through a heat exchanger, wherein at least a first portion of said air downstream of said heat exchanger passes through at least one pipe and into a manifold radially outward of said blade outer air seal, and then passes across said blade outer air seal to cool said blade outer air seal, said diffuser chamber has an outer boundary defined by an outer core housing, said at least one pipe is radially outward of said outer core housing, and said manifold is also outwardly of said outer core housing, said manifold communicates with passages passing through said outer core housing to said blade outer air seal; charactersised in that said passages passing through said outer core housing extend to a radially outer surface of said blade outer air seal and flow in both upstream and downstream locations around said blade outer air seal; and said air flowing upstream of said blade outer air seal is routed through holes in a seal portion of said blade outer air seal to cool adjacent a leading edge of said blade outer air seal and the air passing downstream of said blade outer air seal passes through holes in said seal portion of said blade outer air seal to cool adjacent a trailing edge of said blade outer air seal. a compressor section (24; 101), a combustor, and a turbine section, said combustor having a radially outer surface defining a diffuser chamber radially outwardly of said combustor, said turbine section including a high pressure turbine first stage blade having an outer tip, and a blade outer air seal positioned radially outwardly of said outer tip; and a tap for tapping air having been compressed by said compressor section (24; 101) and being passed through a heat exchanger, wherein at least a first portion of said air downstream of said heat exchanger passes through at least one pipe and into a manifold radially outward of said blade outer air seal, and then passes across said blade outer air seal to cool said blade outer air seal, said diffuser chamber has an outer boundary defined by an outer core housing, said at least one pipe is radially outward of said outer core housing, and said manifold is also outwardly of said outer core housing, said manifold communicates with passages passing through said outer core housing to said blade outer air seal; charactersised in that said passages passing through said outer core housing extend to a radially outer surface of said blade outer air seal and flow in both upstream and downstream locations around said blade outer air seal; and said air flowing upstream of said blade outer air seal is routed through holes in a seal portion of said blade outer air seal to cool adjacent a leading edge of said blade outer air seal and the air passing downstream of said blade outer air seal passes through holes in said seal portion of said blade outer air seal to cool adjacent a trailing edge of said blade outer air seal.