Questions For Tom — Isaac Martin

let \(E_0 \to E_1\) be a complex of vector bundles over an algebraic stack \(Y\) on which \(T\) acts with no fixed part (i.e. assume the \(E_i\) are moving). I don’t think \(e(E) = e(E_1)/e(E_0)\) is defined in \(\hat{A}^*_T(Y)\), as suggested on page 7 section 3.1 of the notes, unless we localize at all nonzero characters. Otherwise I don’t see how \(1/e(E_0)\) is defined.
definition of \(S(\mathfrak C)\): the notation suggested by Proposition 5 in the notes suggests that there is some cone/bundle combination giving us some sort of refined Gysin morphism for the map \(\iota:\mathcal Y^T\to \mathcal Y\). I have no idea what the cone here should be. We can still look at the normal cone to the map \(\iota\), but does this necessarily embed into the intrinsic normal bundle or whatever? I don’t know how to define the map \(S\circ \sigma\) appearing in Prop 5, basically

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