We consider a complex smooth projective variety equipped with an action of an algebraic torus with a finite number of fixed points. We compare the motivic Chern classes of Białynicki-Birula cells with the 𝐾$K$$K$-theoretic stable envelopes of a cotangent bundle. We prove that under certain geometric assumptions for example for homogenous spaces, these two notions coincide up to normalization.

中文翻译：

---

余切丛的动机陈类和稳定包络的比较

我们考虑一个复数光滑射影簇，它具有有限个不动点的代数环面的作用。我们将 Białynicki-Birula 细胞的动机 Chern 类别与𝐾$ķ$$K$-余切丛的理论稳定包络。我们证明，在某些几何假设下，例如对于同质空间，这两个概念与归一化一致。