Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes

We construct semi-orthogonal decompositions on triangulated categories of parabolic sheaves on certain kinds of logarithmic schemes. This provides a categorification of the decomposition theorems in Kummer flat K-theory due to Hagihara and Nizioł. Our techniques allow us to generalize Hagihara and Nizioł's results to a much larger class of invariants in addition to K-theory, and also to extend them to more general logarithmic stacks.