( CNN ) The hunt is on for Hayat Boumeddiene , the 26-year-old woman wanted over Thursday 's fatal shooting of a French policewoman . Early reports suggested she might have escaped Friday from a kosher grocery store in eastern Paris as French authorities mounted a rescue operation to free hostages being held there by Amedy Coulibaly , believed to be her boyfriend . However , CNN reports that no witness has publicly said the woman was actually at the scene of the siege , and now sources are saying she left France before the attack on the policewoman . Boumeddiene is believed to have left France for Turkey around January 2 with the final destination of Syria , according to French and Turkish sources . Regardless , photographs of Boumeddiene published by Le Monde show her shooting what appears to be a crossbow in an all-enveloping black niqab . At first glance , this might appear puzzling . After all , jihadist militant organizations support Taliban-style rule , which allows women only a role at home . However , we have seen a number of women from the West , including American citizens , taking an operational role in jihadist terrorist plots , including Colleen LaRose , a Caucasian-American 46-year-old from Pennsylvania , known as `` Jihad Jane , '' who traveled to Europe in 2009 to scope out an attack on Lars Vilks , a Swedish artist who had drawn a cartoon of the Prophet Mohammed 's head on the body of a dog . European women have also played an operational role in jihadist terrorism . Muriel Degauque , a 38-year-old Belgian woman , died when she committed a suicide bombing in Iraq in 2005 . And on May 14 , 2010 , Roshonara Choudhry , a 21-year-old British woman , stabbed Stephen Timms , her local member of Parliament , for his vote in support of the Iraq War . Timms survived the attack . And there is also 31-year-old British citizen Samantha Lewthwaite , who is , according to Interpol , `` wanted by Kenya on charges of being in possession of explosives and conspiracy to commit a felony dating back to December 2011 . '' The Kenyans believe she was part of a terrorist cell that was planning to carry out an attack in Kenya . Lewthwaite is the widow of one of the suicide attackers who set off bombs on London 's transportation system on July 7 , 2005 , killing 52 commuters . All this underscores that the phenomenon of females joining the jihad has become far more common in the past four years , fueled by the Syrian war , which is drawing an unprecedented number of foreign militants from around the globe , including from the West . According to data collected by New America , based on media reports and court documents , of the 455 individuals who have been publicly identified from around the world who have traveled or were arrested while attempting to travel to Syria to fight with a terrorist organization , 36 were women from the West . That 's 8 % . And their average age is , astonishingly , only 18 years . They hail from countries from around the West : Australia , Austria , Belgium , France , Germany , the Netherlands , Spain , Britain and the United States . And in many cases , these Western women are often going to Syria with the fantasy that there they will be able to marry the jihadist militant of their dreams . Several of these aspiring jihadist brides are Americans . In October , three teenage girls from Colorado were intercepted at Frankfurt Airport in Germany as they were trying to make their way to Syria to join ISIS . Their parents tipped off the FBI when they went missing . Another Colorado resident , 19-year-old Shannon Maureen Conley , was arrested at Denver International Airport before she departed on her journey to join an ISIS camp near the Turkish-Syrian border . She planned to marry a member of ISIS whom she had met online . She pleaded guilty in September . Another girl , the 17-year-old sister of Chicago-based Mohammed Hamzah Khan , was allegedly planning to travel with her brother to Turkey and from there to join ISIS . She and her brother were arrested at Chicago 's O'Hare International Airport in October . Khan faces up to 15 years in prison for trying to provide `` material support '' in the shape of his own services to ISIS , while his sister , who is not being named by the government , is a minor and likely wo n't be charged . Finally , there 's Nicole Mansfield , a Michigan resident who left her 18-year-old daughter behind to join rebel forces in Syria . She died in May 2013 fighting , reportedly , with one of the many jihadist militant groups fighting there . It 's a strange kind of jihadist female equal opportunity : You too can be part of the holy war that seeks to install a Taliban-style utopia that will ensure you can never have a job or get an education .
Peter Bergen : Search for Hayat Boumedienne highlights issue of female jihadists . European women have also played an operational role in jihadist terrorism , he says .