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The algebra \\Gamma[x] can be described as an inverse limit as k goes to infinity of the symmetric subalgebra in the exterior algebra \\Lambda(x_1, ...,x_k) in the variables x_1, ..., x_k. We compute the R(G)-algebra structure of the G-equivariant K-theory of \\Omega G in a way which naturally generalizes the classical computation of the ordinary co"},"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":"1206.1835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-06-08T18:51:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8e36de7c6d946cb2b3a8d088b9d66c5ca4bdbb8fa1b0cfeb372d867068764ffb","abstract_canon_sha256":"04bd789a6fc68f80695fc6ad1246390243e3f7aa2a81b6dd20d40dfedb279622"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:55.276445Z","signature_b64":"uvl7IsGM0xd6IgfuU8JsnxLuiHi0+TPHaaqh43+LifnH+FPCZrMFxIjBXfRbi9RsdjrOAnSi0sNLbOs1U9W2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9376df1cf06503fbc5c839fdedac8adfd13d92fd96deaccaac07517c3ca6ed1c","last_reissued_at":"2026-05-18T03:53:55.275650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:55.275650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The product structure of the equivariant K-theory of the based loop group of SU(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Lisa C. 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