YAKUTSK, Siberia -- A sales girl in a tailored suit unwraps a piece of faded paper, and diamonds worth thousands of dollars glitter under the fluorescent lights.


A hush descends on the small circle of women in elegant minks. Fingers with red-painted nails reach out hesitantly.


The scene might be unremarkable in Antwerp or London, but here, in a diamond shop in the heart of the frozen wastelands of Siberia, it seems downright bizarre.


This semiwilderness, known as Sakha, formerly Yakutia, one of the world's most inhospitable regions, used by Russia for centuries as a place of exile for prisoners, produces a fifth of the world's diamonds.


The Yakuts, struggling to keep their Turkic language and traditions since coming under Russian rule in the 17th century, discovered they could be rich more than four decades ago when Russians struck diamonds here.


They lived in poverty as the Russians scooped out some of the world's highest-quality gems from under the frozen earth.


But now, the semiautonomous republic is claiming its stake.


Forget that preserve of Western thinking -- that no big diamond-producing country has a polishing industry, just as no major polishing center produces diamonds.


Sakha, six time zones from Moscow and several hours by air from Tokyo, will one day become a world center with its own cutting industry and trade in rough gems, officials here say.


"We want to be able to deal directly with London and international markets," says Semyon Zelberg, vice president of the Sakha-based Almazy Rossiya-Sakha, the only organization in Russia with a licence to trade rough gems.


Sakha has already opened its first diamond exchange for polished gems. Zelberg says there are plans to set up a trading center for rough diamonds, at present under Moscow's monopoly.


The vast region, six times the size of France with just a million people, is almost completely isolated -- not quite what is needed to move the world's diamond markets.


Supply ships lie marooned in ice on the frozen Lena River. There are no roads out of the capital, Sakha. It is so cold that ordinary boots freeze. People wrap themselves against the cold in furs -- mink, sable and blue fox, all farmed or hunted in Sakha -- and boots made of deerskin.


Houses, some still with no running water or lavatories, have no direct telephone lines to the outside world.


But talking to specialists at the Tuyimaada diamond cutting and marketing center, at what must be the smartest office between the Arctic circle, just north of here, and Lake Baikal, to the south, one feels a world away.


"People who drive Rolls-Royces -- that's our market," says Pyotr Fyodorov, the well-heeled director of one of Tuyimaada's eight polishing factories. "Russian dinosaur plants, with thousands of people, are past. Diamond-cutting is a fashion business. We must deliver what the market wants. We'll catch up with the West in three years."


Behind a creaky metal door with padlocked iron bars, Yakuts cut stones in a smoke-filled room. With average monthly salaries of $150, diamonds remain beyond the reach of many.


But Semyon Popov, a young polisher listening to rap on a Walkman, says he's saved up enough to buy a half-carat stone. "But my wife wants a big one. I tell her to wait a bit."


"Brillianty -- navsegda," diamonds are forever, reads a sign on the wall at a retail sales outlet upstairs. Marketing chief Natalya Solomonova says they can't keep up with demand.


"The internal market in Russia is like a desert. We just throw in diamonds, people keep wanting more," she says. "Before, everything went to Moscow. Our women never knew what a diamond was. Now it's becoming a status symbol." Belgian and Israeli businessmen, Russian banks, the mistresses of Moscow's mafia bosses, and Chechens from the wild Caucasus.


Diamond-cutting, a high-value industry that operates on fine margins, is in its infancy in Sakha, and even officials admit that current turnovers are a joke.


The republic has no trading licence of its own for cut or rough diamonds, and all foreign sales have to go through Moscow.


"Deals take weeks," says Ivan Gotovtsev, head of industrial gems at Almazy Rossiya-Sakha. "We fly to Moscow and pay thousands of dollars to bureaucrats there to speed things up."


Yet Tuyimaada hopes to double the number of its plants to 16, and market 200,000 carats of polished gems in 1995.


Zelberg, whose conglomerate partly owns Tuyimaada, sees cut-gem sales of $200 million for 1995, and $1 billion in a few years.


For Yakuts, a third of the population here, exporting polished stones instead of rough gems is a matter of national pride.


"Only diamonds can provide the wealth we want," says Foreign Economic Relations Minister Vitaly Artimonov. "We need billions and billions of dollars."