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We prove in this paper that exotic aromatic B-series satisfy a universal geometric property, namely that they are characterised by locality and equivariance with respect to orthogonal changes of coordinates. This characterisation confirms that exotic aromatic B-series are a fundamental geometric object that naturally generalises aromatic B-series and B-series, as they share similar equivariance properties. In addition, we provide a classification of the main subsets of the exotic aromatic B-series, in particular the exotic B-series, using different equivariance properties. Along the analysis, we present a generalised definition of exotic aromatic trees, dual vector fields, and we explore the impact of degeneracies on the classification.\n                  <\/jats:p>","DOI":"10.1007\/s10208-024-09668-5","type":"journal-article","created":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T13:02:11Z","timestamp":1723813331000},"page":"1595-1626","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Universal Equivariance Properties of Exotic Aromatic B-Series"],"prefix":"10.1007","volume":"25","author":[{"given":"Adrien","family":"Laurent","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hans","family":"Munthe-Kaas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,16]]},"reference":[{"issue":"4","key":"9668_CR1","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/j.crma.2019.04.008","volume":"357","author":"A Abdulle","year":"2019","unstructured":"A.\u00a0Abdulle, G.\u00a0A. 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