Let
R be a ring. We prove that the homotopy category
K(
R-Proj) is always
À1\aleph_1-compactly generated, and, depending on the ring
R, it may or may not be compactly generated. We use this to give a description of
K(
R-Proj) as a quotient of
K(
R-Flat). The remarkable fact is that this new description of
K(
R-Proj) generalizes to non-affine schemes; this will appear in Murfet’s thesis.