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Abstract LetGbe a linear real reductive Lie group. Orbital integrals define traces on the group algebra ofG. We introduce a construction of higher orbital integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra ofG. We analyze these higher orbital integrals via Fourier transform by expressing them as integrals on the tempered dual ofG. We obtain explicit formulas for the pairing between the higher orbital integrals and theK-theory of the reduced group$$C^{*}$$-algebra, and we discuss their application toK-theory.more » « lessFree, publicly-accessible full text available January 1, 2026
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Abstract We show, under an orientation hypothesis, that a log symplectic manifold with simple normal crossing singularities has a stable almost complex structure, and hence is Spin$$_c$$. In the compact Hamiltonian case we prove that the index of the Spin$$_c$$ Dirac operator twisted by a prequantum line bundle satisfies a $[Q,R]=0$ theorem.more » « less
