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We consider the equivariant quantum differential equation for the projectivespace $P^{n-1}$. We prove an equivariant gamma theorem for $P^{n-1}$, whichdescribes the asymptotics of the differential equation at its regular singularpoint in terms of the equivariant characteristic gamma class of the tangentbundle of $P^{n-1}$. We describe the Stokes bases of the differential equationat its irregular singular point in terms of the exceptional bases of theequivariant K-theory algebra of $P^{n-1}$ and a suitable braid group action onthe set of exceptional bases.  Our results are an equivariant version of the well-know results of B.Dubrovin and D. Guzzetti.

Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space