* Hess shares up 2.7 percent * Hess proceeds $1.8 bln * Lukoil shares down 1.2 pct By Michael Erman and Vladimir Soldatkin NEW YORK/MOSCOW, April 1 (Reuters) - Hess Corp, which has been besieged by activist investors pushing for change at the oil and gas company, said it would sell its Russian unit to Lukoil for $2.05 billion as it works to reshape its sprawling energy business. Lukoil, Russia's second-largest crude oil producer, is buying the unit - called Samara-Nafta - as part of a long-term strategy to stabilize its falling oil output. Hess owns 90 percent of the unit and expects its after tax proceeds will be about $1.8 billion. Samara-Nafta is currently producing 50,000 barrels of oil equivalent per day in the Volga-Urals region of Russia, the company said. Hedge fund Elliott Management, which owns 4.39 percent of Hess' shares, has been clamoring for change at Hess since January, when it launched a campaign to seat five new directors on the board and pitched a plan to break up the company. Hess has since announced plans to exit its retail gasoline, marketing and trading businesses, and assembled its own slate of six new directors for its board. It also announced the sale of assets its interests in the UK North Sea, Texas and Azerbaijan. The company said the total after tax proceeds from these sales will be about $3.4 billion. Chief Executive John Hess said in a statement that the company plans to use most of the future proceeds from the rest of its current asset sale program to return capital to shareholders. Samara-Nafta has around 85 million tonnes of 1 and 2 category oil reserves, classifications similar to probable and proven reserves, Lukoil said. Lukoil's oil production has been on the decline for three years due to an increasing rate of depletion of fields in West Siberia as well as disappointing output at its new deposits in the Timan-Pechora region in northern Russia. The Russian company has also been aggressively increasing its resource base by buying into overseas upstream projects, including the West Qurna-2 field in Iraq. Shares of Hess rose $1.90, or 2.7 percent, to $73.51 in early afternoon trading on the New York Stock Exchange. Lukoil shares were down around 1.2 percent.