On Type II noncommutative geometry and the JLO character

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The Jaffe-Lesniewski-Osterwalder (JLO) character is a homomorphism from K-homology to entire cyclic cohomology. This paper extends the domain of the JLO character to include Type II noncommutative geometry, the geometry represented by unbounded θ-summable Breuer-Fredholm modules; and shows that the JLO character coincides with the Chern-Connes character as a class in entire cyclic cohomolgoy.