* Hermes, Kering fall after HSBC cuts rating * Banks, miners, energy stocks among gainers * Euro zone business growth at 15-year high - PMI * Bank of Ireland falls as government to sell part of its stake (Adds comments, graphic, updates prices throughout) June 23 (Reuters) - European stocks remained below record highs on Wednesday as inflation worries overshadowed data showing a rise in June business activity, while shares in French luxury goods makers tumbled on the back of a ratings downgrade from HSBC. The pan-European STOXX 600 was down 0.7%, with France’s Kering and Hermes falling 3.0% and 1.5%, respectively, as HSBC said the market for luxury goods “might take a break as it really could be as good as it gets”. The broader retail index tumbled 1.3%. The French and German bourses were among the biggest decliners even as data showed a boom in June service sector activity in both countries amid easing coronavirus restrictions. A survey showed that euro zone business growth accelerated at its fastest pace in 15 years in June as the easing of lockdown measures unleashed pent-up demand and drove a boom in the dominant services sector but also led to soaring price pressures. “The further strengthening of the eurozone composite PMI to a 15-year high in June underlines that the economy is rebounding quickly,” said Jack Allen-Reynolds, senior Europe economist at Capital Economics. “However, the strong economic rebound is coming alongside further evidence of intensifying price pressures.” The benchmark STOXX 600 pulled back from all-time highs last week following a surprisingly hawkish tone from the U.S. Federal Reserve on inflation and monetary policy. Economically sensitive sectors including banks, miners and energy have since climbed back up as Fed Chair Jerome Powell reassured markets the central bank would not raise interest rates too quickly based only on the fear of coming inflation. The so-called value stocks were flat to higher by the session’s end, while growth-linked technology stocks were unable to hold on to an early rally tracking a record overnight finish in their U.S. peers. In company news, Pernod Ricard raised its annual profit forecast as the French drinks maker saw a stronger than expected recovery with the removal of COVID-19 curbs. Its shares rose 2.0% to a record high. British group GSK rose 1.0% as it set out plans to turn its consumer healthcare arm into a separately listed company. Bank of Ireland fell 2.0% as Finance Minister Paschal Donohoe said the Irish government would begin to sell down part of its 13.9% shareholding in the lender over the next six months, marking the state’s first sale of any bank shares since 2017. Reporting by Sagarika Jaisinghani and Shreyashi Sanyal in Bengaluru; Editing by Shounak Dasgupta and Gareth Jones Our Standards: The Thomson Reuters Trust Principles.