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We report on a systematic investigation of the initial growth stages of Co on (2x1) reconstructed Ge(111) by means of low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) combined with first-principles density functional theory (DFT) calculations. The key feature of our work is the first experimental observation of non-invasive embedding of individual Co atoms in the Ge(111)(2x1) surface and simultaneously formation of islands of a novel Co/Ge intermixed layer (IL) with Ge-Co surface reconstruction. We find that Co atoms have only a limited mobility when deposited on cold surfaces (Ts < 80 K), and they reside exclusively on top of the upper Ge(111)(2x1) pi-bonded chain rows. Voltage-dependent STM imaging reveals a highly anisotropic electronic perturbation of the Ge surface surrounding the Co atom and pronounced one-dimensional confinement along the pi-bonded chains. DFT calculations of the Co/Ge system show that the Co atoms are actually embedded in the Ge surface, where they occupy a quasi-stationary position in between the 3rd and 4th atomic Ge layer. Calculated STM images based on our DFT model perfectly match the experimental STM images. In addition, we show that the embedded Co atoms can diffuse along the upper pi-bonded chains underneath the Ge surface at Ts > 80K. Co atoms consequently accumulate at atomic steps and domain boundaries as well as at vacancies or adatoms, which act as nucleation centers for Co/Ge ILs. These Co/Ge ILs exhibit a highly ordered atomic structure, having the same periodicity as that of the initial (2x1) reconstruction, but a doubled period along the [2-1-1] direction due to the modified electronic properties of the upper and lower Ge pi-bonded chains.