According to British media reports, the Indian government is currently in the process of asking for the Kohinoor diamond, and other artifacts, back from the UK.
Let sleeping stones lie - Telegraph India
Historic! India plans repatriation of Kohinoor, colonial artefacts
india: India plans repatriation of Kohinoor, colonial artefacts
Britain's Camilla will not wear disputed Koh-i-Noor diamond for
india: India plans repatriation of Kohinoor, colonial artefacts from UK
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India may not get back Kohinoor diamond: Centre [np] : r/india