On the motivic class of the stack of bundles

By K. Behrend, A. Dhillon. 2007

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Indecomposable vector bundles and stable Higgs bundles over smooth projective curves (2014, background): “Y∞ i=1 ζX(q−is). iii) If ν= (r,d) with r>0 then (1ν | 1ν) = q(g−1)(r2−1) q−1 |Pic0(X)| Y∞ i=2 ζX(q−i). Proof. The ﬁrst statement is well known as the Siegel formula, see [HN, Prop. 2.3.4] and also [BD] for a motivic analog. The second statement is also well known but we indicate a proof in the ap”
On the motives of moduli of chains and Higgs bundles (2011, methodology): “Then Behrend and Dhillon define its class as [M] := [X ] [GLn] ∈ K̂0(Var).”