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This question is mainly a reference request.

I was wondering if there exists such a thing as the symmetric product of a quotient stack $[U/G]$, and in particular I would be interested in the motivic class of this object. For example, if $U=\textrm{pt}$ and $G=\mathbb C^\times$, and if one can make sense of $\textrm{Sym}^n(\textrm{B}\mathbb C^\times)$, then one can also write the motivic generating series $$A(t)=\sum_{n\geq 0}\bigr[\textrm{Sym}^n(\textrm{B}\mathbb C^\times)\bigr]\cdot t^n\in K(\textrm{St}_{\mathbb C})[[t]].$$ Has this been studied somewhere?

Thanks!

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    $\begingroup$ In case you're not already aware of this, there is something about that in the paper of Ekedahl arxiv.org/abs/0903.3148 (starting in section 2, in particular on page 5 he talks about symmetric powers of stacks) $\endgroup$
    – Mattia Talpo
    Jan 30, 2017 at 19:52
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    $\begingroup$ This paper seems to elaborate a bit on what Ekedahl does. arxiv.org/abs/1008.5063 $\endgroup$
    – Thomas Poguntke
    Jan 31, 2017 at 11:29
  • $\begingroup$ Thanks a lot for the references, they are indeed helpful! $\endgroup$
    – Andrea Ricolfi
    Feb 2, 2017 at 15:25

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