Common base large signal transfer characteristics
Does this now mean that Vbe = -Vi? Or is it that Vbe = 0 since the base is grounded?


\$V_{be} = V_b - V_e\$

So yes, in your diagram, \$V_{be}\$ is \$-V_i\$.

\$V_{be}\$ is only equal to 0 if the base and emitter are at the same potential.