Context : The 16 Cygni system is composed of two solar analogues with similar masses and ages .
A red dwarf is in orbit around 16 Cygni A , and 16 Cygni B hosts a giant planet .
The abundances of heavy elements are similar in the two stars , but lithium is much more depleted in 16 Cygni B than in 16 Cygni A , by a factor of at least 4.7 .

Aims : The interest of studying the 16 Cygni system is that the two star have the same age and the same initial composition .
The differences currently observed must be due to their different evolution , related to the fact that one of them hosts a planet while the other does not .

Methods : We computed models of the two stars that precisely fit the observed seismic frequencies .
We used the Toulouse Geneva Evolution Code ( TGEC ) , which includes complete atomic diffusion ( including radiative accelerations ) .
We compared the predicted surface abundances with the spectroscopic observations and confirm that another mixing process is needed .
We then included the effect of accretion-induced fingering convection .

Results : The accretion of planetary matter does not change the metal abundances but leads to lithium destruction , which depends upon the accreted mass .
A fraction of the Earth ’ s mass is enough to explain the lithium surface abundances of 16 Cygni B .
We also checked the beryllium abundances .

Conclusions : In the case of accretion of heavy matter onto stellar surfaces , the accreted heavy elements do not remain in the outer convective zones , but are mixed downwards by fingering convection induced by the unstable \mu -gradient .
Depending on the accreted mass , this mixing process may transport lithium down to its nuclear destruction layers and lead to an extra lithium depletion at the surface .
A fraction of the Earth ’ s mass is enough to explain a lithium ratio of 4.7 in the 16 Cygni system .
In this case beryllium is not destroyed .
Such a process may be frequent in planet-hosting stars and should be studied in other cases in the future .