(Updates prices) HONG KONG, Aug 12 (Reuters) - Asian shares retreated on Thursday as worries about Chinese regulatory changes and the spread of the Delta variant of the coronavirus weighed on sentiment despite tame U.S. inflation easing fears the Federal Reserve would rush to reduce support. Those consumer price inflation figures also caused the dollar to retreat against most major currencies and U.S. Treasury yields to edge down overnight, though both were steadier in Asian hours. MSCI’s broadest index of Asia-Pacific shares outside Japan dropped 0.51% in early trading, dragged by a 0.79% decline in Chinese bluechips and a 0.54% fall in the Hong Kong benchmark as weaker-than-expected lending data on the mainland triggered liquidity concerns. Among the biggest decliners was Chinese online insurer ZhongAn which fell 13.47% after state media said China’s banking and insurance regulator would step up scrutiny of the country’s online insurance companies. Nervous traders have been quick to respond to remarks from Chinese state media and officials, after many were surprised by last month"s tougher-than-expected new rules for the private tutoring sector here, one of several regulatory crackdowns that have roiled sectors from technology to property here. “China’s growth is slowing and the recent regulatory oversight issues have presented headwinds for investors which have broader region-wide implications. The Delta variant spread is also worrying given (Asia’s) low vaccination rate,” said David Chao, Global Market Strategist, Asia Pacific (ex-Japan) at Invesco. Japan’s Nikkei bucked the trend, rising 0.35%, and was heading for a fifth straight session of gains, underpinned by solid earnings from domestic companies. U.S. stock futures were little changed, with S&P 500 e-minis down 0.05%, and the pan-region Euro Stoxx 50 futures were down 0.01%. The weaker performance by Asian benchmarks contrasts with the situation elsewhere. On Wednesday the MSCI all-country index , a gauge of stocks across the globe, hit a record high. In comparison the Asian benchmark is down over 10% from its February peak. “The money is just in the U.S. and European markets right now, and that’s our preferred market too,” said Daniel Lam, senior cross-asset strategist, Standard Chartered Wealth Management. Lam pointed to a strong U.S. earnings season and high vaccination rates in the United States and Europe, which meant the spread of the Delta variant of the new coronavirus was having less of an economic impact than in Asia. The Dow Jones Industrial Average and S&P 500 closed at record levels on Wednesday, after the publication of figures showing the consumer price index increased 0.5% last month, the largest drop in month-to-month inflation in 15 months, easing concerns about the potential for runaway inflation. U.S. policymakers are publicly discussing how and when they should begin to trim the massive asset purchases launched by the Fed last year to stabilise financial markets and support the economy through the coronavirus pandemic. The easing of fears about inflation reduces the pressure to taper those asset purchases soon rather than later in the year, after strong employment figures last week had given ammunition to those with a more hawkish tilt. As a result, U.S. Treasury yields fell on Wednesday across most maturities, though trading was choppy. Yields on benchmark 10-year Treasury notes were last 1.3472% compared with a U.S. close of 1.359%. The dollar hovered below a four-month peak against major peers on Thursday, after retreating overnight as yields dropped. Oil largely held on to gains from earlier in the week, U.S. crude dipped 0.03% to $69.23 a barrel. Brent crude was flat at $71.43 per barrel. Gold also held on to overnight gains, with the spot price down 0.1% having risen 1.3% in the previous session. Easing fears about higher interest rates would typically help the non-interest bearing asset.