The aim of this note is to provide detailed information about the Brown-Peterson spectrum BP as obtained from MUQ 2 by the Quillen splitting C8S . In particular, we present convenient polynomial generators for rC.(Bp) and give the fundamental parameters of the structure of BP-homology as explicit expressions in terms of our generators. The paper is organized as follows: in 1. we describe polynomial generators for Kffi'G'.(BP) in terms of the internal structure of the Quillen algebra B=TU.(BP^BP) and describe the right action of K on B in terms of these generators; in 2. we describe the maps (ir^xr). and (~). associated with the factorization ~=~ of the Quillen idempotent ~ :MUQ 2 > MUQ2 , and point out that this describes the coaction of B on BP.(CP n) for all n; in 3. we describe the formal group law over BP in terms of the polynomial generators exhibited in the first section. We shall use the notation of E2] which will be our main reference. All of the results described for p=2 of course have analogues for the Brown-Peterson spectrum for odd primes, but some of the proofs are then quite different.