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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 4th 2020
   • (edited Oct 4th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something <a href="https://ncatlab.org/nlab/revision/equivariant+Chern-Dold+character/1">v1</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern-Dold+character">current</a>

   starting something

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 4th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am expecting that the equivariant Chern character in equivariant K-theory is naturally induced by the [[equivariant rationalization]]-map on the classifying $G$-space for equivaraiant K-theory. Instead, people like to give various fairly involved component-definitions of the equivariant Chern character. That these component definitions are indeed equivalent to the natural definition by rationalization of the classifying $G$-space appears, as a side remark, below the proof of Theorem 5.5 in [Lück-Oliver 01](https://ncatlab.org/nlab/show/equivariant+Chern+character#LueckOliver01). Does any author make this more explicit?

   I am expecting that the equivariant Chern character in equivariant K-theory is naturally induced by the equivariant rationalization-map on the classifying $G$-space for equivaraiant K-theory.

   Instead, people like to give various fairly involved component-definitions of the equivariant Chern character.

   That these component definitions are indeed equivalent to the natural definition by rationalization of the classifying $G$-space appears, as a side remark, below the proof of Theorem 5.5 in Lück-Oliver 01.

   Does any author make this more explicit?