Can Women Lead People in Friday Prayer?

There is a consensus among Muslim jurists that a woman is not allowed to lead men in a Mosque or congregation. Also, she is not allowed to lead people in a Friday Prayer or to deliver the Friday khutbah. She is, however, allowed to lead a congregation consisting only of women.
Sheikh Muhammad Nur Abdullah, President of the Islamic Society of North American (ISNA) and member of the Fiqh Council of North America, states the following:

1. Islamic teachings are based on two things: belief and submission. When it comes to `ibadat (acts of worship), the Prophet (peace and blessings be upon him) taught us to follow his example and not someone else’s. Salah (ritual Prayer) is unanimously agreed to be an act of `ibadah, and the Prophet (peace and blessings be upon him) is reported to have said “Pray as you see me praying.” So the example of the Prophet (peace and blessings be upon him) and the Companions and the generations that came after them have to be followed.
2. The rules of salah should be known from scholars because they know how to interpret the sayings of the Prophet (peace and blessings be upon him). Among those great scholars are `A’ishah (may Allah be pleased with her). Among the rules of salah are the requirements and prerequisites for how to perform it, who can lead the people in salah, and so on.

3. Scholars have put certain conditions for someone to be qualified to lead the people in Prayer. The imam must be a Muslim, sane, adolescent, male, and pure, i.e., have wudu’ (ablution). Women leading men in Prayer is wrong, whether in fard (obligatory) or nafl (supererogatory) Prayers. But if the followers are only women, it is allowed for a woman to lead the Prayer. According to Shafi`is and Hanbalis, a woman can lead other women in Prayer while standing in the middle of the line. According to Malikis, women cannot lead other women in Prayer at all, while the Hanafis say it is makruh or blameworthy.
4. According to the hadith of Umm Waraqah reported in the Sunan of Abu Dawud, the Prophet (peace and blessings be upon him) appointed a muezzin for her, and ordered her to lead her family members in Prayer.
5. The majority of Muslim jurists say that there is no single incident where a woman led a mixed Prayer outside her family members.
Having said that, we cannot find one single proof that women can lead men outside their family members in salah, and going with the hadith “pray as you see me praying”, we cannot innovate a way of performing salah.