Converting CO2 to fuels is required to enable the production of sustainable fuels and to contribute to alleviating CO2 emissions. In considering conversion of CO2, the initial step of adsorption and activation by the catalyst is crucial. In addressing this difficult problem, we have examined how nanoclusters of reducible metal oxides supported on TiO2 can promote CO2 activation. In this paper we present density functional theory (DFT) simulations of CO2 activation on heterostructures composed of clean or hydroxylated extended rutile and anatase TiO2 surfaces modified with chromia nanoclusters. The heterostructures show non-bulk Cr and O sites in the nanoclusters and an upshifted valence band edge that is dominated by Cr 3d- O 2p interactions. We show that the supported chromia nanoclusters can adsorb and activate CO2 and that activation of CO2 is promoted whether the TiO2 support is oxidised or hydroxylated. Reduced heterostructures, formed by removal of oxygen from the chromia nanocluster, also promote CO2 activation. In the strong CO2 adsorption modes, the molecule bends giving O-C-O angles of 127 - 132 degrees and elongation of C-O distances up to 1.30 angstrom; no carbonates are formed. The electronic properties show a strong CO2-Cr-O interaction that drives the interaction of CO2 with the nanocluster and induces the structural distortions. These results highlight that a metal oxide support modified with reducible metal oxide nanoclusters can activate CO2, thus helping to overcome difficulties associated with the difficult first step in CO2 conversion.