We have obtained a deep radio image with the Very Large Array at 6 cm in the Lockman Hole .
The noise level in the central part of the field is \sim 11 \mu Jy .
From these data we have extracted a catalogue of 63 radio sources with a maximum distance of 10 arcmin from the field center and with peak flux density greater than 4.5 times the local rms noise .
The differential source counts are in good agreement with those obtained by other surveys .
The analysis of the radio spectral index suggests a flattening of the average radio spectra and an increase of the population of flat spectrum radio sources in the faintest flux bin .
Cross correlation with the ROSAT/XMM X-ray sources list yields 13 reliable radio/X-ray associations , corresponding to \sim 21 % of the radio sample .
Most of these associations ( 8 out of 13 ) are classified as Type II AGN .

Using optical CCD ( V and I ) and K ^ { \prime } band data with approximate limits of V \sim 25.5 mag , I \sim 24.5 mag and K ^ { \prime } \sim 20.2 mag , we found an optical identification for 58 of the 63 radio sources .
This corresponds to an identification rate of \sim 92 % , one of the highest percentages so far available .
From the analysis of the colour-colour diagram and of the radio flux - optical magnitude diagram we have been able to select a subsample of radio sources whose optical counterparts are likely to be high redshift ( z > 0.5 ) early-type galaxies , hosting an Active Galactic Nucleus responsible of the radio activity .
This class of objects , rather than a population of star-forming galaxies , appears to be the dominant population ( { { } _ { > } \atop { } ^ { \sim } } 50 % ) in a 5GHz selected sample with a flux limit as low as 50 \mu Jy .

We also find evidence that at these faint radio limits a large fraction ( \sim 60 % ) of the faintest optical counterparts ( i . e . sources in the magnitude range 22.5 < I < 24.5 mag ) of the radio sources are Extremely Red Objects ( EROs ) with I-K ^ { \prime } > 4 and combining our radio data with existing ISO data we conclude that these EROs sources are probably associated with high redshift , passively evolving elliptical galaxies .
The six radio selected EROs represent only \sim 2 % of the optically selected EROs present in the field .
If their luminosity is indeed a sign of AGN activity , the small number of radio detections suggests that a small fraction of the EROS population contains an active nucleus .