I would like to know if there are any textbooks on topological $K$-theory that explain the Atiyah-Hirzebruch spectral sequence and use it to compute $KO$ of (real) stunted projective spaces. I know that Dugger's A geometric introduction to K-theory covers these topics, but there are many digressions and lacks a bit of formality (not in the sense that is not well-written, but I think its aim is to expose some topics to experienced readers, not to formally introduce the subjects). Right now my level in $K$-theory is at the long exact sequence / Bott periodicity / fundamental product theorem (basically the first three chapters of Randal-Williams Characteristic classes and K-theory); do you know any book that, starting from my level or below, introduces the two topics I mentioned, with patience and formality?
Update: I searched again more deeply but I keep finding only papers that seem already too advanced. At this point my question is: are there actual textooks that contain AHSS (for topological $K$-theory) and stunted projective spaces (even separately in two books) aside from Dugger's one?