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AG (Algebraic geometry)
Mixed
See also Oriented cohomology, Oriented homology, Oriented Borel-Moore homology, Algebraic cobordism
http://mathoverflow.net/questions/55602/which-cohomology-theories-are-real-and-complex-orientable
http://mathoverflow.net/questions/17010/complex-orientations-on-homotopy
nLab page on Orientable cohomology