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Then C_0(X,\\delta^{-1}) x G is KK-theoretically Poincare dual to (C_0(X,\\delta)\\otimes_{C_0(X)} C_\\tau(X)) xG, where \\delta^{-1} is the inverse of \\delta in the Brauer group. We deduce this from a strengthening of Kasparov's duality theorem RKK^G(X; A,B) \\cong KK^G(C_\\tau(X)\\otimes A, B). As applications we also obtain a version of the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0610044","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-10-02T15:52:43Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"166c4274cab6d2201439b3a2e8bcb9472a8facb50dab99df2deba1049680f912","abstract_canon_sha256":"7c29cf9e558ae2473dae0534539f675d05ca3fd228bf7560fd0ed3e77368547c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:53.217739Z","signature_b64":"QLq4GlGMxddae9V4GdfxBUM0/zgQkcaa2UNAHpUhi4rMyvvKeYm/EKW7jwDx84tgu7XPjUqcW9w8ipRtDGh1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64e554734bd3f8ac433099ee4ef1783f386c52ea76e94865a7a32b75b1da6346","last_reissued_at":"2026-05-18T04:08:53.217293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:53.217293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"KK-theoretic duality for proper twisted actions","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Heath Emerson, Hyun Jeong Kim, Siegfried Echterhoff","submitted_at":"2006-10-02T15:52:43Z","abstract_excerpt":"Let the discrete group G act properly and isometrically on the Riemannian manifold X. Let C_0(X, \\delta) be the section algebra of a smooth locally trivial G-equivariant bundle of elementary C*-algebras representing an element \\delta of the Brauer group Br_G(X). Then C_0(X,\\delta^{-1}) x G is KK-theoretically Poincare dual to (C_0(X,\\delta)\\otimes_{C_0(X)} C_\\tau(X)) xG, where \\delta^{-1} is the inverse of \\delta in the Brauer group. We deduce this from a strengthening of Kasparov's duality theorem RKK^G(X; A,B) \\cong KK^G(C_\\tau(X)\\otimes A, B). 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