Compactifications of ω and the Banach space c0

We investigate for which compactifications gamma omega of the discrete space of natural numbers omega, the natural copy of the Banach space c(0) is complemented in C(gamma omega). We show, in particular, that the separability of the remainder gamma omega\omega is neither sufficient nor necessary for c(0) to be complemented in C (gamma omega) (the latter result is proved under the continuum hypothesis). We analyse, in this context, compactifications of ! related to embeddings of the measure algebra into P (omega)/fin. We also prove that a Banach space C(K) contains a rich family of complemented copies of c(0) whenever the compact space K admits only measures of countable Maharam type.