{
  "abstract": "This is the first in a series of papers extending Roe algebras and coarse index theory to the groupoid-equivariant setting. We introduce some techniques to develop a framework of Roe algebras and their K-theory for spaces equipped with proper actions of étale groupoids. For a fixed étale groupoid G and G-C* -algebra A, we construct a functor KC(-; G, A) from the category of locally compact Hausdorff proper G-spaces and equivariant proper continuous maps to the category of graded abelian groups, which provides a natural receptacle for an equivariant coarse index map. We study the existence of universal modules, an analog of ample modules in non-equivariant setting, and develop a decomposition technique to establish their existence. As an application, we prove that groupoid simplicial complexes satisfying suitable hypotheses admit universal modules.",
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  "article_type": null,
  "arxiv": "2609.37679",
  "author_total": 1,
  "authors": [
    {
      "name": "Kai Mao"
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  "bibtex": "https://research.draconitic.com/paper/4t42tbj8er2rx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37679",
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  "id": "4t42tbj8er2rx",
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  "landing_url": "https://hal.science/hal-05769372v1",
  "language": "en",
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  "pdf_url": "https://hal.science/hal-05769372/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4t42tbj8er2rx.ris",
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      "first_seen": "2026-10-30T12:17:43Z",
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      "native_id": "2609.37679",
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      "url": "https://arxiv.org/abs/2609.37679"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
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  "title": "Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. I",
  "title_text": "Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4t42tbj8er2rx",
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