Understanding the action that comes with $H^1_{cont}(G_K,GL_n(\mathbb{C}_p))$?

Question

I need to look through Sen's "Continuous Cohomology and p-Adic Galois Representations" 1990 paper, but I have confused myself.

What is the $G_K$-action on $GL_n(\mathbb{C}_p)$, that makes it into a $G_K$-module?

He states that "Continuous cohomology refers to a theory in which the modules are given the topology induced by the valuation of the underlying field".

Thanks!