MOSCOW, Jan 11 (Reuters) - The Russian rouble fell against the dollar on Monday on lingering fears of new sanctions and lower oil prices, while the MOEX benchmark stock index hit an all-time high and GDRs in TCS Group, which owns online bank Tinkoff, continued rallying. Hit by the COVID-19 pandemic, a slump in oil prices and concerns about possible new sanctions, the rouble lost about 16% of its value versus the greenback in 2020 and, despite hopes for recovery, has been slow to rebound in early 2021. The Russian currency was 1% weaker against the dollar at 74.91 as of 1414 GMT and had lost 0.5% to trade at 91.01 versus the euro. Russian assets have come under pressure recently after U.S. intelligence agencies said Russia was likely to have been behind a string of hacks identified last month that gained access to several federal agencies. The current political turmoil in the United States also does not promise an easy start of the year for Russia, Rosbank, a subsidiary of Societe Generale, said in a note. “High oil prices and continuing risk-on should support the rouble this week, albeit geopolitical risks and rising chances of tighter monetary policy by the CBR (central bank of Russia) will weigh,” BCS Brokerage said. “We expect the rouble to remain in the current corridor of Rb73-75/$.” A Reuters poll of market experts predicted the rouble will firm in 2021 but will still be far from levels seen in early 2020. Market activity was expected to recover this week after Russia’s long New Year and Orthodox Christmas holidays from Jan. 1 to Jan. 8. Brent crude oil, a global benchmark for Russia’s main export, was down 1.4% at $55.19 a barrel, hovering above levels of around $51.50 seen in late 2020. That did not help the dollar-denominated RTS index, which was down 0.6% at 1,458.1 points. The drop in the rouble pushed the rouble-based MOEX index 0.3% higher to 3,466.3 points. It touched a record high of 3,516.9 earlier in the day. Global depositary receipts (GDRs) in Russia’s TCS Group were up 2.5% in Moscow, extending their steep climb after it announced a decrease in founder Oleg Tinkov’s voting rights. (Reporting by Andrey Ostroukh. Editing by Catherine Evans and Mark Potter)