Question: Awesome as Fuck (marketed as Awesome as F**k or Awesome as **** or Awesome: Live ) is a live album by which American punk rock band, formed in 1986 by lead vocalist and guitarist Billie Joe Armstrong, and bassist Mike Dirnt?

Context paragraphs:
Jason White (musician): Jason White (born November 11, 1973) is an American musician, best known as the current touring guitarist for the American punk rock band Green Day.  He has played as a touring member of Green Day since 1999.  However, in 2012, he was promoted to being an official member of the band before demoting himself back to his touring guitarist role in 2016.  He is also the guitarist/vocalist for the Californian punk band Pinhead Gunpowder, lead guitarist/lead vocalist for California, and co-founder of Adeline Records alongside Billie Joe Armstrong.

21st Century Breakdown: 21st Century Breakdown is the eighth studio album by American punk rock band Green Day.  It is the band's second rock opera, following "American Idiot" (2004), and their first album to be produced by Butch Vig.  Green Day commenced work on the record in January 2006 and forty-five songs were written by vocalist/guitarist Billie Joe Armstrong by October 2007, but the band members did not enter studio work until January 2008.

Green Day related projects: Since 1991, some members of punk band Green Day have branched out past their "main band" and have started other projects with other musicians and have released full-length albums and several EPs.  Notable related projects of Green Day include Billie Joe Armstrong's Pinhead Gunpowder (which also featured Green Day's other guitarist Jason White), The Frustrators in which Mike Dirnt plays bass, and The Network which many speculate has all three members of Green Day, although under stagenames.

Mike Dirnt: Michael Ryan Pritchard (born May 4, 1972), known professionally as Mike Dirnt, is an American musician, songwriter and composer.  He is best known as the co-founder, bassist, backing vocalist and occasional lead vocalist of American punk rock band Green Day.  He has also played in several other bands, including The Frustrators.  His stage name was originally a nickname that his friends from grade school had given him, as he would constantly play "air bass" and make a "dirnt, dirnt, dirnt" noise while pretending to pluck the strings.

George Cole (musician): George Cole (born October 10, 1960) is an American music producer, composer, lyricist, vocalist, session musician, and guitarist.  He fronts his own Gypsy jazz/Uptown Swing band and since early 2014 has been the guitarist for the David Grisman Quintet.  Before his acoustic music endeavors, he played electric guitar for the pop rock band Beatnik Beatch and Big Blue Hearts.  He played on Chris Isaak's platinum Forever Blue album.  Cole is also a teacher, and his students include Billie Joe Armstrong and Mike Dirnt of Green Day; Ethan Roberts, and Danny Jones.

Bill Schneider (musician): William 'Bill' Schneider (born June 17) is an American musician.  He has played bass in the punk rock band Pinhead Gunpowder since 1990, as well as providing vocals and writing the lyrics to the song "Backyard Flames".  He has also been in many other bands such as The Influents, Monsula and Uranium 9v, Sawhorse and The Skinflutes.  Bill was worked as bass tech during the Nimrod era for Mike Dirnt, Green Day's and as guitar tech on their albums "Nimrod" and "Warning", American Idiot, 21st Century Breakdown, Uno Dos Tres, Revolution Radio and was their day to day manager from 2003-2012 for their "American Idiot" and 21st Century Breakdown tours through Uno Dos Tres.  He also owned "Broken Guitars", a guitar shop in Oakland, California with Billie Joe Armstrong.  Bill Still works on the sidelines with the band as well as in the studio.

Awesome as Fuck: Awesome as Fuck (marketed as Awesome as F**k or Awesome as **** or Awesome: Live ) is a live album by the American punk rock band Green Day.  The album was released on March 22, 2011 through Reprise Records.

Green Day: Green Day is an American punk rock band formed in 1986 by lead vocalist and guitarist Billie Joe Armstrong and bassist Mike Dirnt.  For much of the group's career, the band has been a trio with drummer Tré Cool, who replaced former drummer John Kiffmeyer in 1990 prior to the recording of the band's second studio album, "Kerplunk" (1991).  Guitarist Jason White, who has worked with the band as a touring member since 1999, was an official member from 2012 to 2016.

Billie Joe Armstrong: Billie Joe Armstrong (born February 17, 1972) is an American musician, singer, songwriter and actor who is best known as the lead vocalist, primary songwriter, and guitarist of the punk rock band Green Day, which he co-founded with Mike Dirnt.  He is also a guitarist and vocalist for the punk rock band Pinhead Gunpowder and provides lead vocals for Green Day's side projects Foxboro Hot Tubs and The Network.

J.A.R.: "J.A.R." is a song by the American punk rock band Green Day.  The song was a previously unreleased track from the Dookie sessions but it was later featured on the soundtrack to the movie "Angus" in 1995.  The acronym stands for 'Jason Andrew Relva', a childhood friend of Green Day bassist Mike Dirnt.  Jason Relva was born on November 16, 1972 and died at the age of 19 on April 18, 1992 as the result of injuries sustained from a car accident.  Mike Dirnt wrote the song in remembrance of him.

Supporting paragraphs: Awesome as Fuck Green Day
Answer: Green Day