Preheat oven to Broil.
In a medium sauce pan, combine the shredded chicken and 1/2 cup of the barbecue sauce. Heat on medium low heat until chicken is warmed through.
Split english muffins in half and place cut side up on a large baking sheet that has been covered in foil or parchment paper. Place under the broiler for 1 minute or until lightly toasted. Watch to make sure they do not burn.
Lightly brush some barbecue sauce on all four english muffin halves. Place a little of the warmed chicken on each muffin half.
Sprinkle on diced pepper and pineapple. Top with a mound of grated cheese.
Place back on foil or parchment lined baking sheet and back into oven for 2-3 minutes or until cheese is melted and bubbly.