  We give a bordered extension of involutive HF-hat and use it to give an
algorithm to compute involutive HF-hat for general 3-manifolds. We also explain
how the mapping class group action on HF-hat can be computed using bordered
Floer homology. As applications, we prove that involutive HF-hat satisfies a
surgery exact triangle and compute HFI-hat of the branched double covers of all
10-crossing knots.
