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We explore the role of environment in the evolution of galaxies over0.1<z<0.7 using the final zCOSMOS-bright data set. Using the red fraction ofgalaxies as a proxy for the quenched population, we find that the fraction ofred galaxies increases with the environmental overdensity and with the stellarmass, consistent with previous works. As at lower redshift, the red fractionappears to be separable in mass and environment, suggesting the action of twoprocesses: mass and environmental quenching. The parameters describing theseappear to be essentially the same at z~0.7 as locally. We explore the relationbetween red fraction, mass and environment also for the central and satellitegalaxies separately, paying close attention to the effects of impurities in thecentral-satellite classification and using carefully constructed samplesmatched in stellar mass. There is little evidence for a dependence of the redfraction of centrals on overdensity. Satellites are consistently redder at alloverdensities, and the satellite quenching efficiency increases withoverdensity at 0.1<z<0.4. This is less marked at higher redshift, but both arenevertheless consistent with the equivalent local measurements. At a givenstellar mass, the fraction of galaxies that are satellites also increases withthe overdensity. At a given overdensity and mass, the obtained relation betweenthe environmental quenching and the satellite fraction agrees well with thesatellite quenching efficiency, demonstrating that the environmental quenchingin the overall population is consistent with being entirely produced throughthe satellite quenching process at least up to z=0.7. However, despite theunprecedented size of our high redshift samples, the associated statisticaluncertainties are still significant and our statements should be understood asapproximations to physical reality, rather than physically exact formulae.

zCOSMOS 20k: Satellite galaxies are the main drivers of environmental effects in the galaxy population at least to z~0.7