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Chemisorption of CO on the stepped Cu(211) surface is studied within ab initio density functional theory (DFT) and scanning tunneling microscopy (STM) imaging as well as manipulation experiments. Theoretically we focus on the experimentally observed ordered $(2\ifmmode\times\else\texttimes\fi{}1)$ and $(3\ifmmode\times\else\texttimes\fi{}1)$ CO phases at coverages $\ensuremath{\Theta}=\frac{1}{3}$, $\frac{1}{2}$, and $\frac{2}{3}$ monolayer (ML). Also, obtain information for isolated CO molecules that are found randomly distributed at low coverages, we performed calculations for a hypothetical $(3\ifmmode\times\else\texttimes\fi{}1)$ phase with $\ensuremath{\Theta}=\frac{1}{3}$ ML. The adsorption geometry, the stretching frequencies, the work functions, and adsorption energies of the CO molecules in the different phases are presented and compared to experimental data. Initially and up to a coverage of $\frac{1}{2}$ ML, CO adsorbs upright on the on-top sites at step edge atoms. Determining the most favorable adsorption geometry for the $\frac{2}{3}$ ML ordered phase turned out to be nontrivial, both from the experimental and the theoretical point of view. Experimentally, both top-bridge and top-top configurations were reported, whereby only the top-top arrangement was firmly established. The calculated adsorption energies and the stretching frequencies favor the top-bridge configuration. The possible existence of both configurations at $\frac{2}{3}$ ML is critically discussed on the basis of the currently accessible experimental and theoretical data. In addition, we present observations of STM manipulation experiments and corresponding theoretical results, which show that CO adsorbed on top of a single Cu adatom, which is manipulated to a location close to the lower step edge, is more strongly bound than CO on top of a step edge atom.