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Let $R_n= E_n^{hS\\mathbb G_n}$, the homotopy fixed point spectrum under the action of the subgroup $S\\mathbb G_n$ of the Morava stabilizer group where $S\\mathbb G_n$ is the kernel of the determinant homomorphism $\\text{det}:\\mathbb G_n\\to \\mathbb Z_p^\\times$. We show that for a $K(n)$-local space $X$ with a $L_{K(n)}K(\\mathbb Z_p, n+1)$-bundle $P\\to X$, the $P$-twisted $R_n$-theory of $X$ is defined. We show that analogous to twisted K-theory, a universal coefficient type isomorphism holds for 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":"1407.2826","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-10T15:27:50Z","cross_cats_sorted":[],"title_canon_sha256":"abd867819378cc42f42cc5c863240d8a40882360d7fde56b8f27e69f82f5a37b","abstract_canon_sha256":"64b565c65829f266a97ed0921e48dd5281580df83f3652400d93aaf0eafcc327"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:32.424428Z","signature_b64":"Daxho37idJuNuGs+wJKujH4FJOR3+IfNypEsL2aQ12uiYRVjFAdYe8jCFXxWWsG6SGQv/cLL0x40vLOGBfOiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d78e0dd945c743d82e60330f6967e5eed0a5fd4bd12810866fc57b610e45abd0","last_reissued_at":"2026-05-18T02:46:32.424016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:32.424016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Chromatic Analogues of Twisted $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mehdi Khorami","submitted_at":"2014-07-10T15:27:50Z","abstract_excerpt":"We introduce a family of twisted $K(n)$-local theories that behave analogous to twisted K-theory. Let $R_n= E_n^{hS\\mathbb G_n}$, the homotopy fixed point spectrum under the action of the subgroup $S\\mathbb G_n$ of the Morava stabilizer group where $S\\mathbb G_n$ is the kernel of the determinant homomorphism $\\text{det}:\\mathbb G_n\\to \\mathbb Z_p^\\times$. We show that for a $K(n)$-local space $X$ with a $L_{K(n)}K(\\mathbb Z_p, n+1)$-bundle $P\\to X$, the $P$-twisted $R_n$-theory of $X$ is defined. 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