Formal group laws arising from localizations of MU

This is sort of a two part question:

1) In one construction of $BP$, the Brown-Peterson spectrum, one uses this idempotent map of Quillen's, $g:MU_{(p)}\to MU_{(p)}$ and from what I can tell, the image of this map is $BP$. I have not worked through the details of this carefully. I guess the main idea is just using Brown representability on the cohomology theory $g^\ast(MU^\ast_{(p)}(-))$. Anyway, what happens if, instead of looking at Quillen's idempotent map, we just look at the localization map $MU\to MU_{(p)}$? Would the cohomology theory and formal group law thereby produced give us the same information as $BP$ but just in a much more unwieldy form?

2) In general, what effect does localization (at a general homology theory) have on complex orientability, and are there interesting cases in which such orientability is preserved and produces interesting formal groups?

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2) is obvious if the localization map is a map of ring spectra. A complex orientation of $E$ is the same as a map of ring spectra $MU \to E$. – Sean Tilson Jul 6 '12 at 16:30
@Sean, localization always preserves ring structure, so does that necessarily mean the localization map is a map of ring spectra? And I guess I'm asking if there are any interesting formal group laws that come from precisely such maps, though it appears not. – Jon Beardsley Jul 6 '12 at 20:04

Regarding (1), since the localisation map from $\mathbb{Z}$ to ${\mathbb{Z}}_{(p)}$ is injective, and $MU_\ast$ is free over $\mathbb{Z}$, localisation $MU \to MU_{(p)}$ will be injective, and so the image of the localisation map will again be $MU$.
Regarding $(2)$, localisation does preserve complex orientations -- a class $u \in E^2(\mathbb{C} P^\infty)$ is an orientation if its restriction to $S^2$ is a unit in $E^2(S^2) = E_0$. Since the map from a ring into a localisation of the ring carries units to units, the same will hold for any localisation of $E$.
@Jon, do you mean the localisation of the homotopy rings, rather than cohomology rings (that's what we're doing above with $MU$)? If so, in the generality of your original question (i.e., localisation at a homology theory), I think that the answer is no. For instance, localisation at Morava K-theories tends to introduce unexpected negative homotopy groups, even to connective spectra. Localising at a prime, however, is much more reasonable, and has the desired effect on $MU$. Indeed, Sullivan's original localisation of spaces was constructed by localising their homotopy. – Craig Westerland Jul 7 '12 at 21:36