On the K-theory of matroids with Tutte coverings

The aim of this work is to explicitly compute the K-theory of the category of matroids with respect to the covering family of Tutte coverings. In particular, we show that this is equivalent to the K-theory spectrum of the category of graphic matroids on looped forests, with the covering family generated by isomorphisms. Further, we show that this yields an equivalence of $C_2$-spectra.