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Results of P. Baum and A. Connes, along with facts about the Chern character, imply that $K^i_\\Gamma(X) \\otimes \\mathbb{C} \\cong K^i(\\widetilde{X}\\slash\\Gamma) \\otimes \\mathbb{C}$ for $i = 0, -1$. In this note, we present an example where the groups $K^i_\\Gamma(X)$ and $K^i(\\widet"},"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":"1010.6271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-10-29T16:51:19Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"12dd1b4d2ed5c6b8db59cb2ce8e918a5c6aeb771716ffb537dae4dacb8289762","abstract_canon_sha256":"40694d7e0091181bc3f7f4c645b9575210b6b3e0a003d39622cfd75b81aaffe4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:07.179569Z","signature_b64":"7zASDRFpnPtERKrKIBHhglH9L763vbVSRZ/m4GctsMqdtJF4S2I0QxJIWGbLuSS4v1Acxj7wN4guHTSmpnsoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bb7bc72309b68ba7ed668807d454b064d0f3ea6156106ba11b9372059021e60","last_reissued_at":"2026-05-18T04:38:07.179072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:07.179072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant K-theory and the Chern character for discrete groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Efton Park","submitted_at":"2010-10-29T16:51:19Z","abstract_excerpt":"Let $X$ be a compact Hausdorff space, let $\\Gamma$ be a discrete group that acts continuously on $X$ from the right, define $\\widetilde{X} = \\{(x,\\gamma) \\in X \\times \\Gamma : x\\cdot\\gamma= x\\}$, and let $\\Gamma$ act on $\\widetilde{X}$ via the formula $(x,\\gamma)\\cdot\\alpha = (x\\cdot\\alpha, \\alpha^{-1}\\gamma\\alpha)$. Results of P. Baum and A. Connes, along with facts about the Chern character, imply that $K^i_\\Gamma(X) \\otimes \\mathbb{C} \\cong K^i(\\widetilde{X}\\slash\\Gamma) \\otimes \\mathbb{C}$ for $i = 0, -1$. In this note, we present an example where the groups $K^i_\\Gamma(X)$ and $K^i(\\widet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6271","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1010.6271","created_at":"2026-05-18T04:38:07.179149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.6271v1","created_at":"2026-05-18T04:38:07.179149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6271","created_at":"2026-05-18T04:38:07.179149+00:00"},{"alias_kind":"pith_short_12","alias_value":"JO33Y4RQTNUL","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JO33Y4RQTNULU7WW","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JO33Y4RQ","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ","json":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ.json","graph_json":"https://pith.science/api/pith-number/JO33Y4RQTNULU7WWNCAH2RKLAZ/graph.json","events_json":"https://pith.science/api/pith-number/JO33Y4RQTNULU7WWNCAH2RKLAZ/events.json","paper":"https://pith.science/paper/JO33Y4RQ"},"agent_actions":{"view_html":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ","download_json":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ.json","view_paper":"https://pith.science/paper/JO33Y4RQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.6271&json=true","fetch_graph":"https://pith.science/api/pith-number/JO33Y4RQTNULU7WWNCAH2RKLAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JO33Y4RQTNULU7WWNCAH2RKLAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ/action/storage_attestation","attest_author":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ/action/author_attestation","sign_citation":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ/action/citation_signature","submit_replication":"https://pith.science/pith/JO33Y4RQTNULU7WWNCAH2RKLAZ/action/replication_record"}},"created_at":"2026-05-18T04:38:07.179149+00:00","updated_at":"2026-05-18T04:38:07.179149+00:00"}