This study investigates the influence of the Galactic Cosmic Rays (GCRs) on the atmospheric composition, temperature and dynamics by means of the 3-D Chemistry Climate Model (CCM) SOCOL v2.0. Ionization rates were parameterized according to CRAC:CRII (Cosmic Ray induced Cascade: Application for Cosmic Ray Induced Ionization), a detailed state-of-the-art model describing the effects of GCRs in the entire altitude range of the CCM from 0-80 km. We find statistically significant effects of GCRs on tropospheric and stratospheric NOx, HOx, ozone, temperature and zonal wind, whereas NOx, HOx and ozone are annually averaged and the temperature and the zonal wind are monthly averaged. In the Southern Hemisphere, the model suggests the GCR-induced NOx increase to exceed 10% in the tropopause region (peaking with 20% at the pole), whereas HOx is showing a decrease of about 3% caused by enhanced conversion into HNO3. As a consequence, ozone is increasing by up to 3% in the relatively unpolluted southern troposphere, where its production is sensitive to additional NOx from GCRs. Conversely, in the northern polar lower stratosphere, GCRs are found to decrease O-3 by up to 3 %, caused by the additional heterogeneous chlorine activation via ClONO2 + HCl following GCR-induced production of ClONO2. There is an apparent GCR-induced acceleration of the zonal wind of up to 5 m s(-1) in the Northern Hemisphere below 40 km in February, and a deceleration at higher altitudes with peak values of 3 m s(-1) around 70 km altitude. The model also indentifies GCR-induced changes in the surface air, with warming in the eastern part of Europe and in Russia (up to 2.25 K for March values) and cooling in Siberia and Greenland (by almost 2 K). We show that these surface temperature changes develop even when the GCR-induced ionization is taken into account only above 18 km, suggesting that the stratospherically driven strengthening of the polar night jet extends all the way down to the Earth's surface.