The tough-tackling Argentina international was brought into the Etihad Stadium by Pellegrini as cover for the injured Vincent Kompany.
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"I have struggled in life and those difficulties define me. I am a hard worker."
Demichelis is looking forward to linking up with manager Pellegrini for a third time in his career following successful spells working together in Argentina and Spain.
"There's a mutual trust and respect between us," the defender remarked of the Chilean. "We have known each other for many years and worked together at River Plate, where we became champions.
"We worked together again at Malaga for two successful years and now life has given us a third chance .
"Manuel was an important part in this. He trusts in me after those two years at Malaga. I want to repay on the pitch the confidence shown by the club and the coaching staff."