Within a two-component approach to high T c copper oxides including polaronic couplings, we identify the pseudogap phase as the onset of polaron ordering. This ordering persists in the superconducting phase. A huge isotope effect on the pseudogap onset temperature T* is predicted and in agreement with experimental data. The anomalous temperature dependence of the mean square copper -oxygen ion displacement observed above, at and below T c stems from an s-wave superconducting component of the order parameter, whereas a pure d-wave order parameter alone can be excluded.The phase diagram of high temperature superconducting (HTS) copper oxides includes antiferromagnetism at zero or small hole doping followed by a spin glass phase, which coexists for a limited doping regime with superconductivity, and finally superconductivity alone at larger doping. Overlaid is the so called pseudogap phase which, for much of the doping regime, onsets at much higher temperatures T* than the other phases. The pseudogap phase is rather ill-defined since it is identified in various ways in different experiments, depending on the properties probed by specific experiments, and by the spatial and temporal resolution of the probes. Theoretically, till now, no consensus about the origin of this phase has been reached, and, in addition, it remained unclear which role this phase plays for HTS's. Here we show that polaron formation is the origin of this phase where their coherence defines its onset temperature T*. This phase is anticipated through the slowing down of the combined electron -lattice displacement which starts far above T*. The involvement of electron -lattice interactions in the pseudogap phase formation has been firmly established experimentally by two different techniques and on two different cuprate families by showing that a large isotope effect on T* is present [1,2] which is sign-reversed as compared to the one on the superconducting transition temperature T c . These experiments, which probe charge ordering are, however, in contrast to experiments which probe the spin channel, as, e.g., NQR [3], where the isotope effect on T* is small and has the same sign as the one on T c . Both data together thus provide compelling evidence that the pseudogap phase is a multicomponent phase where spin and charge ordering coexist. Another important indication of strong and unconventional electron-lattice interactions stems from EXAFS and ion channeling data [4 -7], where strong local deviations in the Cu-O bond lengths from the average one have been observed. The Cu-O-Cu bond length splits into two different lengths separated by 0.06 . This splitting is probably dynamical and can be associated with a local double-well potential reminiscent of ferroelectricity [8]. These anomalies appear first at T* and are characterized by an unusual upturn in the mean square relative copper -oxygen displacement ) ( 2 T σ . A