A fragile ceasefire in Turkey has threatened to fall apart this week, as conflict flared again between the government and the militant Kurdistan Workers' Party. On Tuesday, Turkey's President Recep Tayyip Erdogan announced that a peace process between the two groups was no longer possible. Recent days have seen government jets striking the militants' camps in reprisal for a car bomb attack on Turkish soldiers. Until just a few years ago, the Kurdistan Workers' Party, aka the PKK, was at the center of a bloody battle for Kurdish autonomy from the government in Ankara. The latest spate of violence could derail hopes for a resolution to the fighting, which has killed an estimated 40,000 people since it began in the mid-1980s. Who Are The PKK? The PKK is an ethno-nationalist, Marxist-Leninist group that was founded in 1974 with the goal of establishing an autonomous state for the Kurdish people in Turkey. Kurds make up almost 20 percent of the country's population of over 74 million and, like their fellow Kurds in Syria and Iraq, have long sought independent statehood. Abdullah Ocalan, who has led the PKK since its inception, commands a fervent following and is the single most important figure in the organization. While the PKK doesn't represent all Kurds in Turkey, it does garner popular support. Large-scale conflict with Turkey's government started in 1984 when the PKK launched an armed insurgency against the state. Fighting in southern Turkey claimed thousands of lives on both sides during that early period. It further escalated in the 1990s with the PKK's use of suicide bombing as a tactic. In 1997, the United States placed the group on its list of foreign terrorist organizations, where it remains today. Yet in the 1990s, the group also began to dial back its desire for a fully independent state. The PKK spawned offshoots in Syria with the Kurdish Democratic Union Party, also known as the PYD, and its armed wing, the People's Protection Units or YPG. The latter militia was involved in the defense of the Syrian town of Kobani against Islamic State attackers, a battle in which the U.S. supported the YPG with airstrikes. That episode offered a showcase into how convoluted the alliances in Turkey and Syria can be. The Leader Is Captured Turkish authorities finally caught up with Ocalan in 1999, capturing him in Kenya's capital of Nairobi with help from U.S. intelligence. Before his arrest, the PKK leader had left his residence in Syria and traveled from nation to nation -- including Italy, Greece, Germany and Russia -- aided by sympathizers of the Kurdish independence movement. Turkey's state security court first sentenced Ocalan to death. But following enormous, violent protests from the Kurdish population, not just in Turkey but elsewhere in Europe, his sentence was commuted to life imprisonment. Ocalan is housed in Imrali prison, which is located on an island off Istanbul and where he was the only prisoner until 2009. The PKK went into organizational decline after Ocalan's capture, something that analysts cite as a rare successful case study in how targeting leaders can degrade militant groups. A Peace Process The Turkish government and the PKK made a number of attempts to begin a peace process throughout the 2000s, including holding secret meetings between 2009 and 2011 in Oslo. President Erdogan announced the start of peace talks with Ocalan in 2012, and in early 2013 the latter signaled an immense shift in PKK policy by calling for a ceasefire with Turkish authorities. “From a period of armed resistance, a door has been opened to democratic struggle,” Ocalan wrote in a letter from prison. A shaky ceasefire began after Ocalan's announcement. While some isolated attacks had occurred in the years since, there was cautious optimism about resolving the conflict. The government sought disarmament and withdrawal of PKK forces, while the Kurds wanted more language and cultural rights within Turkey as well as a degree of autonomy. But the civil war in Syria exacerbated tensions, with Kurds expressing anger at the government's lack of support for the hard-fought defense of Kobani. PKK militants further viewed Turkey as supporting Islamic State attacks against the Kurds and accused the government of breaking the domestic ceasefire in 2014. Violent protests against the state erupted once again in the south of Turkey. Violence Surges Again After an Islamic State suicide bombing killed over 30 Kurdish activists in the southern town of Suruc on July 20, the PKK blamed the government for not preventing the attack and declared the ceasefire over -- although Ocalan has not issued such a statement. Two days later, a PKK-linked car bombing killed two Turkish soldiers whom hardliners from the group accused of colluding with the Islamic State. In retaliation, Turkey launched airstrikes against PKK camps in northern Iraq and Islamic State militants in Syria, as well as rounding up alleged supporters from both groups. On Tuesday, Erdogan announced that continuing the peace process was impossible. All of this comes at a time when the liberal, Kurdish-based People's Democratic Party (HDP) is a rising force in Turkey's politics. The party denies affiliation with the PKK, but Erdogan has accused them of being in cahoots. Analysts say that the government's true agenda in its renewed campaign against the PKK may be to tamp down support for the HDP ahead of possible November elections. Also on HuffPost: -- This feed and its contents are the property of The Huffington Post, and use is subject to our terms. It may be used for personal consumption, but may not be distributed on a website.