On the $K$-theoretic logarithmic double ramification class

The logarithmic double ramification cycle is the virtual fundamental class of the locus where a line bundle on a family of curves is fiberwise trivial. We construct a K-theoretic logarithmic double ramification class and prove a product formula and a ${\mathrm{G}\mathrm{L}}_r(\mathbb{Z})$-invariance property. We also give an explicit formula for this class in terms of a Grothendieck polynomial via a novel $K$-theoretic Thom–Porteous formula for vector bundles on algebraic stacks.